# Recommendations Toward Measurement of

Roadload Forces for Heavy Duty Automotive

Applications

for the Office of Transportation & Air Quality United States Environmental Protection Agency



# April 2010 Peter Z. Janosi

### 2 

# Table of Contents Background............... .............. ..................... .......Page 3 Objective........................ ....................................Page 3 Overview of Analyses............... ................. ...... .......Page 4 Analysis a)... **Support for J2263, conv ersion from**  **J126 3**  **.........** 

# .......Page 5 Analysis b)... **A simulation using J2263 principles** 

# .....................Page 5 Analysis c)... **Effects of anemometer placement** 

# .......................Page 6 Analysis d)... **Anemometer calibration** 

# ...............................Page 7 Analysis e)... **A discussion of recently acquired data** 

# ..................Page 10 Overall Reco mmendations ... ................................. ....Page 1 2 Appendix A ..................... ....................... ...... ....... Page 1 4 Appendix B ..................... ....................... .............Page 1 7 Appendix D ......... ....................... .........................Page 1 9 Appendix E ..................... ....................... .............Page 21

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# Background The US EPA has regulated Light Duty vehicle emissions and fuel economy since the 1970’s with verificati on pro cedures in place requiring methods of road force measurements in order to set the emissions dy namometer absorber loading. The practical approach adopted to initialize the dy namometer load determination was the track coastdown method, which relies on vehicl e deceleration as the primary indicator of road force resistance. Over the years various improvements in the coastdown procedure and analys e s have evolved, particularly thanks to F. T. Buckley, who introduced on-board anemometry

with inventive instrument c alibrati on and data reduction methods (ABCD An Improved Coast Down Test and Analys is Method, SAE paper 950626) . With the advent of Heavy Duty vehicle emissions regulations consideration of state - of -the - art road force procedure s unique to Heavy Duty operation is now desirable. 

# Objective Our purpose will be to institute a coast down procedure able to meaningful ly assess aerodynamic and mechanical drag associated with Heavy Duty tractor/trailer configurations and design feature devices . Ultimately these assessments encourage te chnical efficiency

improvements by

quantification of fuel economy and emissions impact in determined driving cycles. In particular the procedure requires capability in... a) ...measuring road force (agents which impede vehicle forward motion) at varying speeds b) ...separation of aerodyn amic and mechanical losses (desirable , may not be essential) c) ...provision of relevant statistics to establish the levels of measurement capability The procedure must be deployable for... a) ...extensive and/or massive Heavy Duty tractor/trailer combinations b) ...varying wind/temperature conditions c) ...public road operation in the presence of same -way and opposing traffic

### 4



# Overview ... **of Analyses** B ased on theoretical simulations and utilizing concepts and assumptions c ontained within SAE procedure J2263 it is demonstrable that road force measurements can be reliably obtained in a restrictive environment because... a) ...J2263 is the accepted credible methodology for determining road force b) ... the voluminous data being obtained may be filtered/omitted for any concern of validity (e.g. environmental or instrumentation anomalies) c) ...the positioning of instrumentation is not critical within reasonable limits d) ...a robust “on-the - fly” instrument calibration technique is being proposed which results in progressive improvement to the calibration factors with subsequent data collection, or may

use carry- forward factors during future tests, if the instrumentation has not been disturbed. e) ...Heavy Duty Class 6 data obtained by EPA in second half of 2009 utilizing GPS and ultrasonic anemometer technology is valid and useable for the determination of baseline f

orces on several configurations. Class 8 results obtained by EPA are more problematic and are discussed for resolution.

### 5



# Analysis a) ... **Support for J2263 , conv** **ersion from J1263**  Appendix A supports the J2263 method conceptually by demonstration of a “ least squares ” solution example, as well as derivation of a formula which convert s J2263 to equivalent J1263 results. Recommendations: a1) J2263 methods should be used as the rational approach for neutral coastdown data reduction . a2) J1263 offers no advantage over J2263, ( even from a testing convenience standpoint) , although evidence suggests the two -term force characterization is sufficient for Heavy Duty vehicles . 

# Analysis b) ... **A simulation using J2263 principles** Appendix B demonstrates that in theory valid results may be obtained from J2263 data over any speed range, any direction of travel, and for any inclusion/omission o f data that is discretionary

to the analyst. The least- squares solution does not require continuous sampling, even spacing or fixed data size. Recommendations: b1) Preliminary

screening (visual plotting) of observed force versus velocity is desirable to view unexpected force trends . These may be caused by

traffic interference, instrument signal failure, sudden wind change, or may result from unexpected drag due to brakes or neutral transmission operation. b2) The examples above justify omission of the raw data applying to the speed range of the anomaly in question . In the event of unexpected but consistent behavior at the same road speed run after r un , the data should be retained, in order not to compromise dy namometer coastdown results, if those are necessary to finalize the process. If the test plan uses several pass es to accumulate the dataset then results will not be compromised by

discretionary

data elimination.

### 6

Recommendations: c1) Placement of the anemometer should be approximately at the centroid of the frontal area between 2 and 4 meters in front. The location is not extremely critical to the quality of results obtained. c2) To prevent unnecessary recalibration of the anemometer it is best to leave it in one undisturbed installation until all tests are complete. Re - installation will require recalibration, as discussed in the next section.

Anemometer placement far from the front of the vehicle will indicate  True air speed vector at this location  True yaw angle at this location  These are conditions that may not be true at the vehicle As the anemometer is positioned closer to the front of the vehicle, vehicle air “blockage” effects will  Dimini sh the observed air speed measurement  Exaggerate the observed yaw angle measurement 

# Analysis c) **... Effects of Anemometer Placement** 

Road Speed Observed Air Speed Vectors Pressure profiles from vehicle air blockage Observed Yaw Angles

### 7



# Analysis d) ... **Anemometer calibration** Appendix D demonstrates that the anemometer can be calibrated without need for steady speed passes (as directed by J2263). The calculated calibration values for speed sensitivity

and yaw offs et angle may be in fact more accurate than b y using the steady speed method. As shown in Analysis c) corrections are required for observed (measured) air speed and yaw angles because the vehicle is generally slowing the apparent air speed more in its direction of travel and less in the perpendicular direction . The vector diagrams below are shown to illustrate a proposed “on-the - fly” calibration model which determines the sensitivity

of the anemometer measurement to true air speed, and to a lesser extent measure s true wind speed and direction :

wind sin (attack) attack wind cos(attack) wind

Vair Vroad attack ya w off wind Vroad ya w true ya w off ya w true



### Definitions for Model V a 

### : Air speed (measured) Vr 

### : Road speed (measured assumed true) NOTE: Road speed values must be assigned negative when the opposing direction data is used  Wind attack angle

 (to be solved) w: Wind speed

 (to be solved) Vector Relationships With the Wind

Vector Relationships Against the Wind

### 8 NOTE: Wind speed and attack angle values will retain their same sign regardless of the direction  Air speed calibration factor

 (to be solved) m 

###  Yaw angle (measured)  t 

###  Yaw angle (true )   

###  Yaw angle offset (

to be solved) Model Equations  2 Va 2 = (V r2 + 2 w cos( 

###  )*V r + w2 ) Ca l eq 1 tan( 

###  t ) = w sin( 

###  ) /[V r + w cos( 

###  )] Cal eq 2 

###  0 = 

###  t - 

### m Cal eq 3 Using the method of least squares a solution matrix can be constructed to solve for the calibration and conditions’ unknowns in Cal eq 1 : A complete derivation of the solu tion matrix follows: The summation of incremental errors squared for “i” observations is

2 1 i n i 

###  

# 

 

### = 

# 

 n i 1 

### [  2 Va i 2

- (V r i 2 + 2 w cos( 

###  )*V r i + w2 )] 2 Setting the partial derivatives of the error- squared to zeros... 

### /  2 2 1 i n i 

###  

# 

 

### = 

# 

 n i 1 

### 2 [  2 Va i 2

- (V r i 2 + 2 w cos( 

###  )*V r i + w2 )] 1 * Va i 2 = 0 

### / [- 2 w cos( 

###  )] 2 1 i n i 

###  

# 

 

### = 

# 

 n i 1 

### 2 [  2 Va i 2

- (V r i 2 + 2 w cos( 

###  )*V r i + w2 )] 1 * V r i = 0 

### / [- w2 ] 2 1 i n i 

###  

# 

 

### = 

# 

 n i 1 

### 2 [  2 Va i 2

- (V r i 2 + 2 w cos( 

###  )*V r i + w2 )] 1 * 1 = 0 In matrix form this appears as... 

# 

 n i 1 

### V a2 

# 

 n i 1 

### Vr 

# 

 n i 1 

### 1  2 

# 

 n i 1 

### Vr2 

# 

 n i 1 

### V a2 

### Vr 

# 

 n i 1 

### Vr2 

# 

 n i 1 

### Vr 

### - 2 w cos( 

###  ) = 

# 

 n i 1 

### Vr 3 

# 

 n i 1 

### V a4 

# 

 n i 1 

### V a2 

### Vr 

# 

 n i 1 

### V a2



### -w2 

# 

 n i 1 

### V a2 

### Vr2

### 9

...and red uces to : 1 0 0  2 

### = X1 0 1 0 - 2 w cos( 

###  ) 

### = X2 0 0 1 -w2 

### = X3 where X1,2,3 are the values for the unknowns as determined by the matrix reduction. From solution of the wind factors above, the yaw offset porti on can be solved by Cal eq 2 and Cal eq3 i.e. 

# 

 n i 1 tan( 

###  t ) i = 

# 

 n i 1 w sin( 

###  ) /[V r i + w cos( 

###  )] 

### tan( 0 ) = [ 

# 

 n i 1 tan( 

###  t ) i - 

# 

 n i 1 tan( 

### m ) i ] / 

# 

 n i 1 [1 + tan( 

###  t ) i tan(

### m ) i ] 

### Application of the calibration factors... The values of  and 

###  0 are then used to correct ALL measured air speed and measured yaw angle data for subsequent use in the J2263 analysis. True air speed = Measured air speed measured * 

###  True yaw angle = Measured yaw angle +  0 

### Appendix D contains numerical solutions of the form above b y trying various subsets of real data obtained from runs “ CD4 ” and “ CD5 ” on an EPA Class 6 vehicle . The corresponding J2263 - like solutions for the force c oefficients are also provided. Recommendations d1) Anemometer calibration i.e. scaling to true air speed and using a yaw angle offset correction is essential to obtain useful force coefficients. d2) In the absence of a steady- speed warmup the “on - the - fly” calibration technique is proposed. Conceptually it may be superior to the “steady” method in that the air speed as it varies with road speed brings in data over a wider speed domain which is more conducive for good calibration. The method will work for any combination of coastdown, acceleration or cruise data. d3 ) The underlying assumption in any calibration scheme is that the wind direction and speed do not vary

significantly

during the data sampling. More data is usually desirable but a sampling se ssion extended over time may introduce wind conditions’ changes that may confound the calibration results. More research is required to conclude

### 10

an optimum sampling scheme, but this should not delay any current coastdown test plans, as all available data will be reviewable for useful calibrations. d4) When the calibration factors have been determined and the instrument installation has not been disturbed, it is possible to apply the calibration factors to any tests commencing or retroactively to any prior tests deemed to require “better” cals. Averaging cal factors from several (undisturbed!) sessions may be appropriate, although a closer look at the mathematics of averaging is prudent. 

# Analysis e) ... **A discussion of recently acquired data** This is analysi s of data obtained from (5) pairs of coastdowns performed on a Class 8 vehicle. The focus is a comparative evaluation of several calibration and force models described below. Method “pg1” a) uses a scaling technique to determine the anemometer speed calibration i.e. the average ratio of road speed to the longitudinally indicated air speed is used to correct the air speed. b) the anemometer center line yaw offset , and use of yaw measurements was ignored because higher speed yaw readings did not indicate a significant change to the longitudinal air component. c) the force model determines two coefficients: Force = Am 

### + C a 

### V air2 

### Method “pg2” is s ame as “pg1” except for the force model: Force = Am 

### + B m 

### Vroad 

### + C a 

### V air 2 

### Method “pg3” is same as “pg1” except for the force model: Force = Am 

### + B m 

### Vroad 

### + C m 

### Vroad 2 

### + C a 

### Vair2 

### Method “pj1” a) uses the calibration method as described in Analysis d) b) the force model used is Force = Am 

### + C a 

### V air2 

### (1 + P yaw2 

### ) cos (yaw) this includes an additional parameter to account for cross wind effects Method “pj2” is same as “pj1” except for the force model:

Force = Am 

### + B m 

### Vroad 

### + C a 

### V air2 

### (1 + P yaw2 

### ) cos (yaw) Method “pj3” is same as “pj1” except for the force model:

Force = Am 

### + B m 

### Vroad 

### + C m 

### Vroad 2 

### + C a 

### V air2 

### (1 + P yaw2 

### ) cos (yaw) Method “pj4” is same as “pj3” except the force model does not use the yaw coefficient “P”: Force = Am 

### + B m 

### Vroad 

### + C m 

### Vroad 2 

### + C a 

### V air2 

### cos (yaw)

### 11

Method “pj5” is same as “pj4” except the force model does not use any yaw correction :

Force = Am 

### + B m 

### Vroad 

### + C m 

### Vroad 2 

### + C a 

### V air2 

### All eight methods were applied against various subsets of data used in the calibration calculation and subsets (usually different) for the force calculation. Numerical results and data subset descriptions are found in Appendix e). Summary of results: a) coefficient determinations show that models in pg1 and pj1 contain sufficient coefficients to describe the vehicle motion. Models pg2 and pj2, although producing the lowest R- squared stati stics also produced the most unexpected values for coefficients due to a large negative Bm term. When the models are supplemented with inclusion of a Cm term (e.g. pg3), they produces similar results as pg1 and pj1. Summary items below will address onl y models pg1 and pj1. b) R- squared statistics are generally low due to high scatter in the raw data. The worst R- squared were produced from data in the mid- speed range (45 - 35 mph).For consideration: Additional filtering may be applied to the raw data. c) pg alw ays produces a lower speed calibration factor “Beta” than pj. The EPA Class 6 evaluations demonstrated a promising value for Beta at 1.06. Prior experience with many s maller vehicles typically show Beta around 1.05. The Class 8 “pg” models are producing c onsiderably less than that value, and “pj” models produce higher. At best, when certain subset s of cal data are considered, pj is 2% higher than pg, producing a 5% difference in total force at high speed, or about 9% difference in the drag coefficient interpretation. On the other hand pg produces more realistic drag if Class 8 can be characterized at about .7 Cd with 100 sq ft frontal area. d) Confidence interval statistics show both pg and pj models very similar, despite the large force difference mentione d above. The statistic (and the R- squared) partly relies on the observed force data as compared to the predicted force data. The “observed” force data is regressed for different two interpretations of Vair 

### (different between pg and pj.) This leaves the s ignificance of the confidence interval somewhat dubious for judging the true difference in the models. e) Experiments using increased speeds produced higher Beta values for any model. pg produced Beta as high as 1.08 at 60 to 50 mph, and as low as 1.01 at 30 to 20 mph. For consideration: A calibration model using a higher order polynomial fit with road speed. Also a theoretical Beta calculated from first principles using speed and proximity of the anemometer installation would be useful.

### 12

f) Using some cal data subsets the pj method was unable to produce cal coefficients. The solution matrix becomes unresolved when computing wind^2 as negative, or cosine values greater than 1. The probable cause for this is that significant wind speed and direction changes oc cur when opposite direction data is considered together. (Another words the assumption for similar opposing direction conditions is weak.) g) It should be noted that the Class 8 vehicle is significantly larger than the Class 6 which produced more expecte d results. The size of Class 8 and the predominance of cross winds during the test session may be cause(s) of the difficulty in a definitive characterization of the Class 8 results. For consideration: Additional data obtained with the same installation in the presence of predominantly head/tail winds. 

# Overall Reco mmendations Given that to date some difficulty persists with the Class 8 analys is the recommendations below include follow up for resolution as well as general procedural recommendations. Some of these may be deemed as beyond the current practical scope of this project, but are worthy of consideration, especially a new comprehensive calibration model that is reliable in all wind conditions . a) If possible the Class 8 vehicle should be run again in the presence of predominantly

head/tail winds, with as close to as possible the same anemometer installation. Positioning of a second anemometer may enhance evaluation of the anemometer(s) calibration with respect to road speeds and proximity to the vehicle. This data combined with first principles models may provide a definitive calibration procedure. b) Relatively

high head/tail winds are desirable for test sessions , unless a better comprehensive calibration model is developed. c) An on-the - fly calibrati on technique is preferred, which reduces data gathering during warm-up, provided a credible calculation is used. Quickly collecting data in two directions is desirable to maintain the underlying assumption that the winds have not changed significantly in opposing directions. The use of existing software is encouraged to aid in selection of data subsets used in the calibration determination. Each pair of runs used will generate a unique Beta and Yaw offset (as well as wind speed and direction averages.) The calibrations coefficients can be averaged, one for Beta, one for offset, to be used as universal factors applied to the measured air speed data. d) Preview all raw data and remove suspect data points affected by possible traffic or instrumentation hick-ups . e) Filter the data to at least 1 Hz or less. f) Discard adjacent pairs of runs, if anomalies are found over significant speed ranges in one or both directions.

### 13

g) Find the regression coefficients for the model Force = Am 

### + C a 

### V air2



### . The yaw model is not required during principally head/tail wind conditions. h) Find the confidence intervals for all data points, by which 3 - sigma data outliers may be identified and removed. i) Determine the new regression coefficients and correct the coefficients to mechanical and air density standards as prescribed in J2263. j) Further investigation for a better calibration model is required to accommodate all wind speeds and directions comprehensively . (One experimental model should investigate the introduction of a yaw measurement correction, and possibly anemometer instrument threshold parameters, similar to the existing J2263 practice.

### 14 **APPENDIX A**

**A pplications Using**  **Least Squares Techniques** Many data reduction analyses (e.g. SAE J1263 and J2263) use a least squares method to solve regression coefficients for a desired model. For simplicity the first example below illustrates solution to a “contrived” problem: In this case we will assume that our vehicle decelerates (demonstrates a f orce “F” acting on it against direction of motion, which is directly measurable b y an accelerometer) and we suspect it has a mechanical loss coefficient constant “a” and an aerodynamic coefficient “c” which acts with the air speed squared. Air speed is ro ad speed “V” plus a head wind “w”. A special test track only points into the wind, and the wind is always a constant, but we do not know the intensity of this constant wind or the drag coefficients that characterize the vehicle. The model to describe the test is written as: F i 

### = a + c (Vi 

### + w) 2 

### i referring to the ith 

### observation; F i 

### ,Vi 

### are known; a, c, w unknown Expanded a + c Vi 2 

### + 2cwVi 

### + cw2



### - F i 

### = 0 Recognizing that not every data point (or likely any data point) will ever behave perfectly with respect to its model (except in a contrived student project) there will be a residual error 

###  i 

### assoc iated with every observation. In this case the Method of Least Squares will find the best a, c, and w which minimizes the summation o f the squares of 

###  i 

### for n data points.

2 1 i n i 

###  

# 

 

### = i

n i 

### F [ 1 

# 

 

### - (a + c Vi 2 

### + 2cwVi 

### + cw2 

### ) ] 2

### 15

The unknowns can take the form of “c” which correlates with Vi 2 

### , “2cw” which correlates with Vi 

### and a lump “a + cw2 

### ” which shows up “n” times. Taking the partials of the error squared with respect to these unknowns and setting them to zero provides the se 3 solution equations. d/dc 2

1 i n i 

###  

# 

 

### = 2 i n i 

###  

# 

 1 

### Vi 2 

### = 

# 

 n i 1 

### F i

### Vi 2



### – c Vi4



### - 2cwVi 3



### - (a+ cw2 

### ) Vi 2 

### = 0 d/d(2cw) 2

1 i n i 

###  

# 

 

### = 2 i n i 

###  

# 

 1 

### Vi 

### = 

# 

 n i 1 

### F i

### Vi 

### – c Vi 3



### - 2cwVi 2



### - (a+ cw2 

### ) Vi 

### = 0 d/d(a+cw2 

### ) 2

1 i n i 

###  

# 

 

### = 2 i n i 

###  

# 

 1 

### 1 = 

# 

 n i 1 

### F i 

### – c Vi 2



### - 2cwVi 

### - (a+ cw2 

### ) = 0 The same equations are shown below with the V and F summations that are linear coefficients of the unknowns in the top row. [c 2cw (a+ cw2 

### ) ] 

# 

 n i 1 

### Vi 2 

### + 

# 

 n i 1 

### Vi 

### + 

# 

 n i 1 

### 1 = 

# 

 n i 1 

### F i 

# 

 n i 1 

### Vi 3 

### + 

# 

 n i 1 

### Vi 2 

### + 

# 

 n i 1 

### Vi 

### = 

# 

 n i 1 

### F i

### Vi 

# 

 n i 1 

### Vi4 

### + 

# 

 n i 1 

### Vi 3 

### + 

# 

 n i 1 

### Vi 2 

### = 

# 

 n i 1 

### F i

### Vi 2 

### Normalizing each row and adding or subtracting rows from each other eventually leads to... 1 0 0 = c 0 1 0 = 2 c w 0 0 1 = a+ cw2 

### All three unknowns have been solved b y “least squares”. The next example demonstrates how J1263 coefficients can be directly calculated from J2263 coefficients. **Another Application...**

### 16

“Least squares” is very

robust in its utility. If you replace discrete 

# 

 n i 1 

### f i 

### with continuous 

#  vi vf 

### dV V f ) ( 

### (as if infinite and perfe ct data sampling existed) then it is possible to quantify the true relationship between EPA AC55B direction (using SAE J1263 methodology) i.e. Force = A + C V2 

### , to force described b y Force = a + bV +cV2 

### (SAE J2263 or even higher order models) So if the small abc’s are more accurate depictions of motion coefficients then we might ask what are the less accurate capital A and C values you expect from a test? Least squares described by a continuous integral error gives you the exact answers.

2 

#  vi vf 

###  

### dV= 

#  vi

vf 

### [ (A + C V2 

### )

– (a + bV + c V2 

### ) ] 2 

### dV Taking the partials of the error squared with respect to A (=1) and C (=V2 

### ) and then integrating gives two equations. Notice that initial velocity Vi 

### and final velocity

V f 

### influences the answer (and that makes sense). This convention of notation is V j 

### = (Vi j



### – V f j 

### ) / j to describe the quantity from integration expressions with limits. Jumping ahead: A V 1 

### + C V 3 

### = a V 1 

### + b V2 

### + c V 3 

### A V 3 

### + C V 5 

### = a V 3 

### + b V4 

### + c V 5 

### and this solves for A and C, for comparison where it crosses the abc curve , where they are the most different, etc, in case that might be relevant in a dy no cycle or for manufacturers’/ independent laboratory audit reasons . In the case of J1263 construction, usually tested between 60 and 20 mph, using units of lbf and mph the values are: A = a + 18.69 b C = c + 0.0123 b

### 17 **APPENDIX B**  This Appendix demonstrates that valid results may be obtained from J2263 data over any speed range, any direction of travel, and for any inclusion/omission of data that is discretionary

to the analyst. Method: An imaginary “test” vehicle of know mechanical and aerody namic behavior is constructed and obeys the laws of motion as solved by the exact differential equation. Various wind speeds are imposed on it, as well as random selection of data ranges. Discrete “ data” is generated and subjected to the least- squares statistical approach inherent to J2263 to solve for the vehicle’s motion coefficients to be compared . Constructed data (one direction) with analys is is shown below:

Model: Force= ma ss * dV/dt= A +C*(V+w) 2 Solution for the d ifferential equation of motion: t= m ass / sqrt( AC) * {arctan[sqrt(C/A)*(v0+w)] -

arctan[sqrt(C/A)*(v+w)}]

C= 0.02 w (wind speed)= 10 v0 (initial road speed)= 60 >>These are given A= 30 m (m ass)= 100 >>These are given t v mi d v m dvdt (m id v + w) 2 (m id v + w) 4 (m id v + w) 2 *m dvdt tim e road

speed avg spd t to

t+2 force 0 60.00 58.75 - 124.52 4727.22 2234658 9.76 - 588648.83 2 57.51 56.33 - 117.97 4399.64 19356840.82 - 519045.10 4 55.15 54.03 - 111.98 4099.87 16808939.49 -459108.82 6 52.91 51.85 - 106.48 3824.88 14629680.12 -407285.74 8 50.78 49.77 - 101.43 3572.03 12759405.45 - 362304.53 10 48.75 47.78 - 96.77 3 339.05 11149236.27 - 323119.46 12 46.82 45.89 - 92.47 3123.93 9758919.91 - 288865.90 14 44.97 44.08 - 88.49 2924.92 8555147.93 - 258825.41 16 43.20 42.35 - 84.80 2740.48 7510232.44 - 232398.24

### 18

18 41.50 40.69 - 81.38 2569.25 6601058.20 - 209081.44

... ... ... ... ... ... ...

... ... ... ... ... ... ... 72 11.55 11.16 - 38.95 447.70 200432.90 - 17439.61 74 10.77 10.39 - 38.31 415.60 172720.94 - 15922.39 76 10.00 9.63 - 37.70 385.18 148364.74 - 14522.80 78 9.25 8.88 - 37.13 356.37 126998.53 - 13231.10 80 8.51 8.14 - 36.58 329.08 108295.29 - 1203 8.46 82 7.77

sum s> - 2611 69072 177547648 - 5622542 count> 41 The Solution Matrix:

41.00 69071.60 - 2611.26 69071.60 177547647.96 - 5622542.40 1 1684.67 - 63.69 1 2570.49 - 81.40 0.00 885.81 - 17.71 0 1 - 0.02000 = - C Matches the assumption 1 0 - 30.00316 = -A Matches the assumption 

### A summary

of experiments that use subsets of the data above (and in the opposing direction of travel) is shown below . Wi nd An y - 10 10 com bined 10 - 10 Count An y 41 41 82 25 17 Data speed selection: Range 1 from An y 60 60 60 60 40 Range 1 to An y 21 8 com bined 40 20 Range 2 from --- 20 Range 2 to --- 8 C= - 0.02000 - 0.02000 - 0.02000 - 0.02 - 0.02000 - 0.02000 A= - 30 - 30.00124 - 30.00316 - 30.0025 - 30.00258 - 30. 00251 

### Conclusion: Very similar coefficients are reproduced regardless of the sample size, direction of travel or the speed range. This is an important realization allowing for omission of data for situations such as traffic pass -by or instrument signal anomalies.

### 19 **APPENDIX D**  The method described in Analysis produced the following results for the anemometer calibration factors for different subsets of data acquired from a pair of coastdowns as well as the resulting force coefficients when the various cals are applied. An abbreviated form of the J2263 coastdown force equation was used for simplicity :

Force = A + B V + Cm V2 

### + Ca Va2 

### (1 + P yaw2 

### ) **Note: Reference to “Both” indicates data was combined bor both directions.** Cal strategy> Used all 4 & 5 data for cal Ignore<20mph Wi nd 6.093293 mp h 7.928648 Attack 115.7914 deg 101.4327 Beta 1.062205 1.066991 Offset - 1.19148 deg - 3.24974

Run 4.1 Run 5.1 Both.1 Run 4.2 Run 5.2 Both.2 A 436.3463 379.5714 394.7492 4 10.5905 367.7773 374.815 B 1.200654 1.772625 3.880628 1.427175 2.457135 4.159128 C 0.15293 0.134544 0.115162 0.157856 0.12189 0.117002 Cm - 0.23486 - 0.72589 - 0.22715 - 0.20561 - 0.73221 - 0.29913 Ca 0.387793 0.860432 0.342309 0.363468 0.854105 0.416136 P 27.86152 5.14759 19.10935 66.84297 14.70565 53.4537

Forces> > > > > > Velocity Run 4.1 Run 5.1 Both.1 Run 4.2 Run 5.2 Both.2

10 463.6459 410.7521 445.0716 440.6478 404.5377 428.1064 20 521.5314 468.8416 518.4263 502.2763 465.6759 504.7982 30 610.003 553.8398 614.8134 595.4758 551.1922 604.8903 40 729.0605 665.7469 734.2327 720.2465 661.0864 728.3827 50 878.7041 804.5628 876.6844 876.5882 795.3585 875.2754 60 1058.934 970.2875 1042.168 1064.501 954.0086 1045.568 70 1269.749 1162.921 1230.68 5 1283.985 1137.037 1239.262 Cal strategy> Use end of run 4, beginning of 5 Only use 40 - 60 mph

### 20 - 0.11041 Wi nd 4.800524 3.217302 Attack 101.8186 2.020941 Beta 1.055687 1.038228 Offset -4.57364 - 6.30057

Run 4.3 Run 5.3 Both.3 R un 4.4 Run 5. 4 Both. 4 A 438.3461 380.6439 394.235 445.261 386.2523 400.4836 B 0.38259 1.514545 3.423691 0.222481 1.271014 3.371765 C 0.174886 0.156469 0.136984 0.187549 0.196747 0.153646 Cm - 0.20821 - 0.81113 - 0.36523 - 0.21247 - 0.77227 - 0.33229 Ca 0.38 3092 0.967599 0.502215 0.40002 0.969017 0.485933 P 16.79252 0.841667 11.39115 5.858074 - 2.1287 1.583424

Forces> > > > > > Velocity Run 4.3 Run 5.3 Both.3 Run 5.1 Run 5.2 Both.5

10 459.6606 411.4363 442.1703 466.2408 418.6371 449.5659 20 515.9 523 473.5224 517.5023 524.7304 490.3714 529.3773 30 607.2211 566.9023 620.231 620.73 601.4551 639.9179 40 733.467 691.5759 750.3565 754.2394 751.8882 781.1877 50 894.6902 847.5434 907.8787 925.2588 941.6708 953.1867 60 1090.89 1034.805 1092.798 1133.78 8 1170.803 1155.915 70 1322.068 1253.36 1305.113 1379.827 1439.284 1389.372 

## Forces **Ob ta**  **in ed**  **Wi th**  **U ni**  **que Cal**  **s**

0 200 400 600 800 1000 1200 1400 1600

0 20 40 60 80 **Vel oci**  **ty [mp**  **h] F** **o r** **c e** **[ l** **b f** **]** 

### Both. 1 Both. 2 Both. 3 Both. 4 4 3 2, 1

### 21 **APPENDIX E**  A comparison of the results for a Class 8 vehicle using various calibration methods, forc e models and selections of data follows : **#1 Cal data captures end of prior run, then beginning of run in opposite direction**  Run # For Cal From To For Data From To Direction 1 1 60 20 1 2 1 40 20 1 60 20 1 3 1 60 40 1 60 20 - 1 4 1 40 20 1 60 20 - 1 5 1 60 40 1 60 20 1 6 1 40 20 1 60 20 1 7 1 60 40 1 6 0 20 - 1 8 1 40 20 1 60 20 - 1 9 1 60 40 1 60 20 1 10 1 60 20 - 1 Wh en a run # is selected for pg cal, the first ten data points are used for the yawoffset ya woffset calculation Models: pg Force = Am + Bm Vroad + Cm Vroad2 + Ca Vair2 (some coeffs are absent where indicated) pj Force = Am + Bm Vroad + Cm Vroad2 + Ca Vair2 (1 + P yaw2) cos(yaw)

pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.04128 1.04128 1.04128 1.10346 1.10346 1.10346 1.10346 1.10346 Attack deg ----------- - ---------- ---------- 80.5525 80.5525 80.5525 80.5525 80.5525 Wi nd speed ------------ ---------- ---------- 13.2519 13.2519 13.2519 13.2519 13.2519 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.83178 -

3.83178 -

3.83178 - 3.83178 ---------- Am 317.284 465.943 3 17.285 317.249 465.957 317.232 317.315 317.285 Bm ------------ - 8.58774 - 5.5E 05 --------- - -

8.59788 0.00108 0.00105 - 5.5E 05 Cm ------------ ---------- - 1.3E 06 ---------- ---------- - 1.3E 06 - 1.3E - 06 - 1.3E 06 Ca 0.1377 0.25279 0.1377 0.12249 0.22463 0 .12248 0.12277 0.12262 P ------------ ---------- ---------- 0.88649 1.46752 0.87968 ----------- ---------- R- sqrd 0.32504 0.33701 0.32504 0.32504 0.33703 0.32504 0.32504 0.32504 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 372.364 395.305 372.364 3 66.245 383.852 366.244 366.444 366.331

### 22 25 403.346 409.245 403.346 393.804 391.405 393.807 394.073 393.92 30 441.213 435.824 441.213 427.489 410.189 427.494 427.841 427.64 35 485.966 475.042 485.966 467.298 440.205 467.304 467.747 467.491 40 537.603 526 .901 537.603 513.231 481.453 513.239 513.791 513.472 45 596.125 591.398 596.125 565.288 533.933 565.297 565.975 565.585 50 661.532 668.536 661.532 623.47 597.643 623.479 624.296 623.828 55 733.824 758.313 733.824 687.777 672.586 687.785 688.757 688.202 60 813.001 860.73 813.001 758.208 758.76 758.215 759.356 758.708 J1263 Am 317.284 306.297 317.284 317.249 306.122 317.252 317.334 317.284 J1263 Ca 0.1377 0.14716 0.1377 0.12249 0.11888 0.12249 0.12278 0.12262

Confidence Intervals given Road Speed alph a at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 9.58755 9.50219 9.58754 9.58754 9.50206 9.58756 9.58759 9.58754 25 6.87269 6.8115 6.87269 6.87269 6.81141 6.8727 6.87272 6.87269 30 4.15783 4.12082 4.15783 4.15783 4.12076 4.15784 4.15785 4.15783 35 1.44298 1.43013 1.44298 1.44298 1.43011 1.44298 1.44298 1.44298 40 1.27188 1.26055 1.27188 1.27188 1.26054 1.27188 1.27188 1.27188 45 3.98673 3.95124 3.98673 3.98673 3.95118 3.98674 3.98675 3.98673 50 6.70159 6.64192 6.70159 6.70159 6.64183 6.7016 6. 70162 6.70159 55 9.41645 9.33261 9.41644 9.41644 9.33248 9.41646 9.41649 9.41644 60 12.1313 12.0233 12.1313 12.1313 12.0231 12.1313 12.1314 12.1313



### Ro **ad Force Com** **par isons** 

0 100 200 300 400 500 600 700 800 900 1000

0 20 40 60 80 **Ro ad** **Spe ed** **[m ph]** **F o** **r c** **e [** **l b** **f ]**  pg-1 pg-2 pg-3 pj-1 pj-2 pj-3 pj-4 pj-5

**#2 Same as #1 for cal, fewer runs for force** Run # For Cal From To For Data From To Direction

1 1 60 20 1 2 1 40 20 1 3 1 60 40 1 60 20 - 1 4 1 40 20 - 1

### 23 5 1 60 40 1 6 1 40 20 1 7 1 60 40 - 1 8 1 40 20 - 1 9 1 60 40 1 10 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.04128 1.04128 1.04128 1 .10346 1.10346 1.10346 1.10346 1.10346 Attack deg ------------ ---------- ---------- 80.5525 80.5525 80.5525 80.5525 80.5525 Wi nd speed ------------ ------------ ------------ 13.2519 13.2519 13.2519 13.2519 13.2519 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3 .83178 - 3.83178 -

3.83178 - 3.83178 ------------ Am 266.602 439.255 266.603 249.197 309.605 249.139 266.831 266.603 Bm ------------ - 10.3182 -4.8E - 05 ------------ - 3.46713 0.00335 0.00126 -4.8E - 05 Cm ------------ ---------- - 1.4E - 06 ---------- ---------- - 3.3E 07 - 1.4E - 06 - 1.4E - 06 Ca 0.16352 0.30472 0.16352 0.12456 0.1697 0.12452 0.14568 0.14561 P ------------ ---------- ---------- 78.6957 50.0059 78.731 ----------- ---------- R- sqrd 0.4048 0.41868 0.4048 0.43093 0.432 0.43092 0.40479 0.4048 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 332.011 354.781 332.011 299.022 308.144 299.014 325.13 324.847 25 368.803 371.752 368.803 327.048 328.992 327.047 357.915 357.61 30 413.772 403.96 413.772 361.302 358.325 361.306 397.984 397.653 35 466.917 451.404 466.917 401.785 396.143 401.791 445.337 444.977 40 528.238 514.084 528.238 448.495 442.447 448.502 499.975 499.582 45 597.735 591.999 597.735 501.434 497.236 501.439 561.897 561.467 50 675.408 685.151 675.408 560.601 560.51 560.602 631.102 630.633 55 761.257 793.54 761.257 625.995 632.269 625.991 707.593 707.08 60 855.282 917.164 855.283 697.618 712.514 697.606 791.367 790.807 J1263 Am 266.602 247.441 266.602 249.197 245.151 249.202 266.855 266.602 J1263 Ca 0.16352 0.17781 0.16352 0.12456 0.12706 0. 12456 0.1457 0.14561

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 20.1067 19.8707 20.1067 19.6603 19.6418 19.6604 20.1068 20.1067 25 14.2471 14.0799 14.2471 13.9308 13.9177 13.9309 14.2472 14.2471 3 0 8.38753 8.28911 8.38752 8.20134 8.19359 8.20135 8.38757 8.38752 35 2.52795 2.49829 2.52795 2.47184 2.4695 2.47184 2.52797 2.52795 40 3.33162 3.29253 3.33162 3.25766 3.25459 3.25767 3.33164 3.33162 45 9.19119 9.08334 9.19119 8.98717 8.97868 8.98718 9.1 9125 9.19119 50 15.0508 14.8742 15.0508 14.7167 14.7028 14.7167 15.0509 15.0508 55 20.9103 20.665 20.9103 20.4462 20.4269 20.4462 20.9105 20.9103 60 26.7699 26.4558 26.7699 26.1757 26.151 26.1757 26.7701 26.7699

### 24 **Ro ad Force**  **Com par**  **isons**

0 100 200 300 400 500 600 700 800 900 1000

0 20 40 60 80 **Ro ad** **Spe ed** **[m ph]** **F o** **r c** **e [** **l b** **f ]**  pg-1 pg-2 pg-3 pj-1 pj-2 pj-3 pj-4 pj-5

**#3 Fewer cals, fewer runs for force** Run # For Cal From To For Data From To Direction 1 1 60 20 1 2 1 40 20 1 3 1 60 40 1 60 20 - 1 4 - 1 5 1 6 1 7 - 1 8 - 1 9 1 10 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 B eta 1.01151 1.01151 1.01151 1.09515 1.09515 1.09515 1.09515 1.09515 Attack deg ------------ ---------- ---------- 80.6788 80.6788 80.6788 80.6788 80.6788 Wi nd speed ------------ ---------- ---------- 13.7271 13.7271 13.7271 13.7271 13.7271 Yaw offset de g - 1.391 - 1.391 - 1.391 - 3.2609 - 3.2609 - 3.2609 - 3.2609 ---------- Am 266.602 439.255 266.603 249.24 311.213 249.18 266.766 266.603 Bm ------------ - 10.3182 -4.8E 05 ---------- -

3.55546 0.00353 0.0017 -4.8E 05 Cm ------------ ---------- - 1.4E 06 -------- -- --------- - - 3.4E 07 - 1.4E - 06 - 1.4E 06

### 25

Ca 0.17329 0.32292 0.17329 0.12936 0.17598 0.12931 0.14786 0.14783 P ------------ ---------- ---------- 98.8836 62.492 98.93 ----------- ---------- R- sqrd 0.4048 0.41868 0.4048 0.43042 0.43154 0.43041 0.40479 0.4 048 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 335.917 362.06 335.917 300.984 310.496 300.975 325.944 325.734 25 374.907 383.126 374.907 330.089 332.315 330.088 359.222 358.995 30 422.561 420.338 422.561 365.663 362.932 365.666 399.892 399.649 3 5 478.88 473.697 478.88 407.704 402.349 407.71 447.955 447.693 40 543.863 543.201 543.863 456.213 450.565 456.22 503.411 503.129 45 617.51 628.851 617.51 511.19 507.58 511.195 566.261 565.957 50 699.822 730.647 699.822 572.635 573.394 572.636 636.503 63 6.176 55 790.798 848.589 790.799 640.548 648.006 640.542 714.138 713.787 60 890.439 982.678 890.44 714.929 731.419 714.914 799.167 798.79 J1263 Am 266.602 247.441 266.602 249.24 245.117 249.245 266.798 266.602 J1263 Ca 0.17329 0.19601 0.17329 0.12936 0 .13225 0.12936 0.14788 0.14783

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 20.1067 19.8707 20.1067 19.6692 19.6497 19.6692 20.1068 20.1067 25 14.2471 14.0799 14.2471 13.9371 13.9233 13.9371 14.2472 14.2471 30 8.38753 8.28911 8.38752 8.20501 8.1969 8.20503 8.38757 8.38752 35 2.52795 2.49829 2.52795 2.47295 2.4705 2.47295 2.52797 2.52795 40 3.33162 3.29253 3.33162 3.25912 3.2559 3.25913 3.33164 3.33162 45 9.19119 9.08334 9.19119 8.99119 8.9823 8.99 121 9.19124 9.19119 50 15.0508 14.8742 15.0508 14.7233 14.7087 14.7233 15.0508 15.0508 55 20.9103 20.665 20.9103 20.4553 20.4351 20.4554 20.9104 20.9103 60 26.7699 26.4558 26.7699 26.1874 26.1615 26.1875 26.7701 26.7699

### 26 **Ro ad Force**  **Com par**  **isons**

0 200 400 600 800 1000 1200

0 20 40 60 80 **Ro ad** **Spe ed** **[m ph]** **F o** **r c** **e [** **l b** **f ]**  pg-1 pg-2 pg-3 pj-1 pj-2 pj-3 pj-4 pj-5

**#4 Same Cal pair measured ov er full speed**  Run # For Cal From To For Data From To Direction 1 1 60 20 1 2 1 60 20 1 3 1 60 20 1 60 20 - 1 4 - 1 5 1 6 1 7 - 1 8 - 1 9 1 10 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.03509 1.03509 1.03509 1.0894 1.0894 1.0894 1.0894 1.0894 Attack deg ------------ ---------- ---------- 79.8673 79.8673 79.8673 79.8673 79.8673 Wi nd speed ------------ ---------- ---------- 12.5395 12.5395 12.5395 12.5395 12.5395 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.32547 -

3.32547 -

3.32547 - 3.32547 ---------- Am 266.602 439.255 266.603 267.223 302.463 267.18 266.67 266.603 Bm ------------ - 10.3182 -4.8E 05 ---------- -

2.11032 0.0026 0.00111 -4.8E 05 Cm ------------ ---------- - 1.4E - ---------- ---------- - 1.5E - - 1.4E - 06 - 1.4E -

### 27 06 07 06 Ca 0.16548 0.30838 0.16549 0.12716 0.15611 0.12712 0.14948 0.1494 P ------------ ---------- ---------- 88.1641 63.6724 88.2001 ----------- ---------- R- sqrd 0.4048 0.41868 0.4048 0.42694 0.42723 0.426 94 0.40479 0.4048 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 332.796 356.243 332.796 318.086 322.699 318.08 326.483 326.361 25 370.03 374.038 370.03 346.696 347.271 346.695 360.121 359.975 30 415.538 407.251 415.538 381.664 379.649 381.667 401.23 2 401.059 35 469.321 455.883 469.32 422.99 419.832 422.994 449.818 449.613 40 531.377 519.934 531.377 470.674 467.82 470.678 505.877 505.636 45 601.708 599.404 601.708 524.716 523.613 524.717 569.41 569.13 50 680.313 694.293 680.314 585.115 587.212 585 .113 640.417 640.094 55 767.193 804.601 767.193 651.872 658.616 651.865 718.897 718.527 60 862.347 930.328 862.347 724.987 737.825 724.972 804.852 804.43 J1263 Am 266.602 247.441 266.602 267.223 263.232 267.228 266.691 266.602 J1263 Ca 0.16548 0.18147 0.16548 0.12716 0.13015 0.12715 0.14949 0.1494

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 20.1067 19.8707 20.1067 19.7291 19.7242 19.7291 20.1067 20.1067 25 14.2471 14.0799 14.2471 13.9796 13.9761 13.9796 14.2471 14.2471 30 8.38753 8.28911 8.38752 8.23002 8.22797 8.23003 8.38756 8.38752 35 2.52795 2.49829 2.52795 2.48048 2.47986 2.48048 2.52796 2.52795 40 3.33162 3.29253 3.33162 3.26906 3.26824 3.26906 3.33163 3.33162 45 9.19119 9.08334 9.19119 9.0186 9.01634 9.0186 9.19123 9.19119 50 15.0508 14.8742 15.0508 14.7681 14.7644 14.7681 15.0508 15.0508 55 20.9103 20.665 20.9103 20.5177 20.5126 20.5177 20.9104 20.9103 60 26.7699 26.4558 26.7699 26.2672 26.2607 26.2672 26.77 26.7699

### 28 **Ro ad Force**  **Com par**  **isons**

0 100 200 300 400 500 600 700 800 900 1000

0 20 40 60 80

**Ro ad**  **Spe ed**  **[ mp**  **h] F** **o r** **c e** **[ l** **b f** **]** pg-1 pg-2 pg-3 pj -1 pj -2 pj -3 pj -4 pj -5

**#4 All cals**  **over full speed** Run # For Cal From To For Data From To Direction 1 1 60 20 1 60 20 1 2 1 60 20 1 3 1 60 20 1 60 20 - 1 4 1 60 20 - 1 5 1 60 20 1 6 1 60 20 1 7 1 60 20 - 1 8 1 60 20 - 1 9 1 60 20 1 10 1 60 20 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.04381 1.04381 1.04381 1.08704 1.08704 1.08704 1.08704 1.08704 Attack deg ------------ ---------- ---------- 79.3688 79.3688 79.3688 79.3688 79.3688 Wi nd speed ------------ ---------- -------- -- 10.9443 10.9443 10.9443 10.9443 10.9443 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.00512 -

3.00512 -

3.00512 - 3.00512 ---------- Am 266.602 439.255 266.603 258.263 423.513 258.242 266.635 266.603 Bm ------------ - 10.3182 -4.8E 05 ---------- -

9.74853 0.0013 5 0.00088 -4.8E 05

### 29

Cm ------------ ---------- - 1.4E 06 ---------- ---------- - 1.3E 06 - 1.4E - 06 - 1.4E 06 Ca 0.16273 0.30324 0.16273 0.14763 0.27066 0.14762 0.15004 0.15005 P ------------ ---------- ---------- 115.17 47.0849 115.168 ----------- ---------- R- sqrd 0.4048 0.41868 0.4048 0.40861 0.42075 0.4086 0.40479 0.4048 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 331.694 354.19 331.694 317.316 336.806 317.315 326.668 326.62 25 368.308 370.829 368.308 350.534 348.961 350.536 360.431 360.38 30 413 .059 402.631 413.058 391.133 374.649 391.137 401.696 401.642 35 465.946 449.594 465.946 439.113 413.871 439.118 450.463 450.407 40 526.969 511.72 526.969 494.475 466.625 494.481 506.731 506.674 45 596.129 589.008 596.129 557.219 532.912 557.224 570.502 570.444 50 673.426 681.459 673.426 627.345 612.732 627.349 641.775 641.715 55 758.859 789.071 758.859 704.852 706.085 704.854 720.549 720.489 60 852.429 911.846 852.429 789.741 812.97 789.739 806.826 806.765 J1263 Am 266.602 247.441 266.602 258.263 242 .288 258.267 266.651 266.602 J1263 Ca 0.16273 0.17633 0.16273 0.14763 0.15075 0.14763 0.15005 0.15005

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 20.1067 19.8707 20.1067 20.0422 19.8353 20.0423 20.1 067 20.1067 25 14.2471 14.0799 14.2471 14.2014 14.0548 14.2015 14.2471 14.2471 30 8.38753 8.28911 8.38752 8.36063 8.27432 8.36066 8.38754 8.38752 35 2.52795 2.49829 2.52795 2.51985 2.49383 2.51985 2.52796 2.52795 40 3.33162 3.29253 3.33162 3.32094 3.28 666 3.32095 3.33163 3.33162 45 9.19119 9.08334 9.19119 9.16172 9.06714 9.16175 9.19121 9.19119 50 15.0508 14.8742 15.0508 15.0025 14.8476 15.0026 15.0508 15.0508 55 20.9103 20.665 20.9103 20.8433 20.6281 20.8434 20.9104 20.9103 60 26.7699 26.4558 26.76 99 26.6841 26.4086 26.6842 26.77 26.7699

### 30 **Ro ad Force**  **Com par**  **isons**

0 100 200 300 400 500 600 700 800 900 1000

0 20 40 60 80

**Ro ad**  **Spe ed**  **[ mp**  **h] F** **o r** **c e** **[ l** **b f** **]** pg-1 pg-2 pg-3 pj -1 pj -2 pj -3 pj -4 pj -5

**#5 All cals over full speed with all force data**  Run # For Cal From To For Data From To Direction 1 1 60 20 1 60 20 1 2 1 60 20 1 60 20 1 3 1 60 20 1 60 20 - 1 4 1 60 20 1 60 20 - 1 5 1 60 20 1 60 20 1 6 1 60 20 1 60 20 1 7 1 60 20 1 60 20 - 1 8 1 60 20 1 60 20 - 1 9 1 60 20 1 60 20 1 10 1 60 20 1 60 20 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.04381 1.04381 1.04381 1.08704 1.08704 1.08704 1.08704 1.08704 Attack deg ---- -------- ---------- ---------- 79.3688 79.3688 79.3688 79.3688 79.3688 Wi nd speed ------------ ---------- ---------- 10.9443 10.9443 10.9443 10.9443 10.9443 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.00512 -

3.00512 -

3.00512 - 3.00512 ---------- Am 317.284 46 5.943 317.285 318.351 465.946 318.341 317.417 317.285 Bm ------------ - 8.58774 - 5.5E 05 ---------- -

8.59097 0.0007 0.00073 - 5.5E 05 Cm ------------ ---------- - 1.3E 06 ---------- ---------- - 1.3E 06 - 1.3E - 06 - 1.3E 06

### 31

Ca 0.13703 0.25157 0.13703 0.12641 0 .23199 0.1264 0.12635 0.12635 P ------------ ---------- ---------- - 3.05696 0.59965 -

3.06015 ----------- ---------- R- sqrd 0.32504 0.33701 0.32504 0.32512 0.33701 0.32512 0.32504 0.32504 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 372.097 394.815 372.097 368.915 386.924 368.915 367.972 367.824 25 402.929 408.479 402.929 397.357 396.168 397.358 396.405 396.253 30 440.613 434.721 440.613 432.12 417.011 432.122 431.156 430.999 35 485.148 473.541 485.148 473.203 449.454 473.205 472.224 472.063 40 5 36.535 524.94 536.535 520.606 493.497 520.609 519.61 519.445 45 594.773 588.917 594.773 574.33 549.14 574.333 573.314 573.144 50 659.863 665.472 659.863 634.374 616.382 634.376 633.335 633.16 55 731.805 754.606 731.805 700.739 695.225 700.74 699.674 699 .494 60 810.598 856.318 810.598 773.424 785.666 773.423 772.331 772.146 J1263 Am 317.284 306.297 317.284 318.351 306.239 318.354 317.43 317.284 J1263 Ca 0.13703 0.14594 0.13703 0.12641 0.12633 0.12641 0.12636 0.12635

Confidence Intervals given Road Sp eed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 9.58755 9.50219 9.58754 9.58698 9.50218 9.58699 9.58756 9.58754 25 6.87269 6.8115 6.87269 6.87229 6.81149 6.87229 6.8727 6.87269 30 4.15783 4.12082 4.15783 4.15759 4.12081 4.15759 4.15784 4 .15783 35 1.44298 1.43013 1.44298 1.44289 1.43013 1.4429 1.44298 1.44298 40 1.27188 1.26055 1.27188 1.2718 1.26055 1.2718 1.27188 1.27188 45 3.98673 3.95124 3.98673 3.9865 3.95123 3.9865 3.98674 3.98673 50 6.70159 6.64192 6.70159 6.7012 6.64192 6.7012 6.7016 6.70159 55 9.41645 9.33261 9.41644 9.41589 9.3326 9.4159 9.41646 9.41644 60 12.1313 12.0233 12.1313 12.1306 12.0233 12.1306 12.1313 12.1313

### 32 **Ro ad Force**  **Com par**  **isons**

0 100 200 300 400 500 600 700 800 900

0 20 40 60 80

**Ro ad**  **Spe ed**  **[ mp**  **h] F** **o r** **c e** **[ l** **b f** **]** pg-1 pg-2 pg-3 pj -1 pj -2 pj -3 pj -4 pj -5

**#6 All cals in mid speed range with all force data**  Run # For Cal From To For Data From To Directi on 1 1 45 35 1 60 20 1 2 1 45 35 1 60 20 1 3 1 45 35 1 60 20 - 1 4 1 45 35 1 60 20 - 1 5 1 45 35 1 60 20 1 6 1 45 35 1 60 20 1 7 1 45 35 1 60 20 - 1 8 1 45 35 1 60 20 - 1 9 1 45 35 1 60 20 1 10 1 45 35 1 60 20 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.0484 1.0484 1.0484 1.0723 1.0723 1.0723 1.0723 1.0723 Attack deg ------------ ---------- ---------- 78.6881 78.6881 78.6881 78.6881 78.6881 Wi nd speed ------------ ---------- ---------- 10.0863 10.0863 10.0863 10.0863 10 .0863 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.04787 -

3.04787 -

3.04787 - 3.04787 ------------ Am 317.284 465.943 317.285 318.04 465.457 318.026 317.266 317.285 Bm ------------ - 8.58774 - 5.5E 05 ---------- -

8.52458 0.0008 0.00039 - 5.5E - 05 Cm ------------ - --------- - 1.3E 06 ---------- ---------- - 1.3E 06 - 1.3E - 06 - 1.3E - 06

### 33

Ca 0.13583 0.24937 0.13584 0.12395 0.23284 0.12395 0.13001 0.12985 P ------------ ---------- ---------- 18.2297 8.07942 18.2127 ----------- ---------- R- sqrd 0.32504 0.33701 0.32504 0.3 256 0.33736 0.32559 0.32504 0.32504 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 371.618 393.936 371.618 367.62 388.103 367.619 369.279 369.224 25 402.181 407.105 402.181 395.508 397.87 395.511 398.533 398.44 30 439.535 432.743 439.535 429.594 419. 279 429.599 434.288 434.148 35 483.681 470.849 483.681 469.877 452.33 469.885 476.544 476.349 40 534.619 521.424 534.619 516.358 497.023 516.368 525.3 525.042 45 592.349 584.467 592.349 569.036 553.359 569.049 580.557 580.228 50 656.87 659.978 656.87 6 27.912 621.337 627.926 642.314 641.906 55 728.183 747.958 728.184 692.985 700.957 693.001 710.572 710.076 60 806.288 848.406 806.289 764.255 792.219 764.272 785.331 784.739 J1263 Am 317.284 306.297 317.284 318.04 306.985 318.041 317.274 317.284 J1263 C a 0.13583 0.14374 0.13583 0.12395 0.12799 0.12395 0.13002 0.12985

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 20 9.58755 9.50219 9.58754 9.58363 9.49964 9.58364 9.58757 9.58754 25 6.87269 6.8115 6.8726 9 6.86988 6.80968 6.86989 6.87271 6.87269 30 4.15783 4.12082 4.15783 4.15613 4.11971 4.15614 4.15784 4.15783 35 1.44298 1.43013 1.44298 1.44239 1.42975 1.44239 1.44298 1.44298 40 1.27188 1.26055 1.27188 1.27136 1.26022 1.27136 1.27188 1.27188 45 3.9867 3 3.95124 3.98673 3.9851 3.95018 3.98511 3.98674 3.98673 50 6.70159 6.64192 6.70159 6.69885 6.64014 6.69886 6.7016 6.70159 55 9.41645 9.33261 9.41644 9.4126 9.33011 9.41261 9.41647 9.41644 60 12.1313 12.0233 12.1313 12.1263 12.0201 12.1264 12.1313 12.13 13

### 34 **Ro ad Force**  **Com par**  **isons**

0 100 200 300 400 500 600 700 800 900

0 20 40 60 80

**Ro ad**  **Spe ed**  **[ mp**  **h] F** **o r** **c e** **[ l** **b f** **]** pg-1 pg-2 pg-3 pj -1 pj -2 pj -3 pj -4 pj -5

**#7 All cals in mid speed range with mid speed force data**  Run # For Cal From To For Data From To Direction

1 1 45 35 1 45 35 1 2 1 45 35 1 45 35 1 3 1 45 35 1 45 35 - 1 4 1 45 35 1 45 35 - 1 5 1 45 35 1 45 35 1 6 1 45 35 1 45 35 1 7 1 45 35 1 45 35 - 1 8 1 45 35 1 45 35 - 1 9 1 45 35 1 45 35 1 10 1 45 35 1 45 35 - 1 pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 Beta 1.0484 1.0484 1.0484 1.0723 1.0723 1.0723 1.0723 1.0723 Attack deg ------------ ---------- ---------- 78.6 881 78.6881 78.6881 78.6881 78.6881 Wi nd speed ------------ ---------- ---------- 10.0863 10.0863 10.0863 10.0863 10.0863 Yaw offset deg - 1.391 - 1.391 - 1.391 - 3.04787 - 3.04787 - 3.04787 - 3.04787 ---------- Am 124.241 598.474 124.244 108.96 608.872 108.938 125.338 124.244 Bm ------------ - 18.0424 - 6.1E 05 ---------- - 19.2275 0.00119 0.00078 - 6.1E 05 Cm ------------ ------------ - 1.7E 06 ------------ ------------ - 1.8E 06 - 1.7E - 06 - 1.7E 06

### 35

Ca 0.2493 0.40202 0.2493 0.24239 0.39942 0.24238 0.23782 0. 23832 P ------------ ---------- ---------- 14.5334 12.0665 14.5316 ----------- ---------- R- sqrd 0.11162 0.14227 0.11162 0.11603 0.15028 0.11603 0.11161 0.11162 Speed pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5

20 223.963 398.433 223.964 205.917 384.091 20 5.913 220.482 219.569 25 280.056 398.675 280.057 260.456 377.824 260.454 273.996 273.191 30 348.614 419.018 348.615 327.113 391.528 327.114 339.401 338.727 35 429.638 459.462 429.638 405.891 425.204 405.893 416.697 416.18 40 523.126 520.006 523.126 496 .788 478.85 496.791 505.884 505.549 45 629.08 600.652 629.08 599.804 552.468 599.807 606.962 606.833 50 747.499 701.398 747.498 714.941 646.057 714.942 719.931 720.033 55 878.383 822.245 878.382 842.197 759.617 842.197 844.791 845.149 60 1021.73 963.19 3 1021.73 981.572 893.149 981.57 981.542 982.181 J1263 Am 124.241 263.066 124.243 108.96 251.432 108.96 125.353 124.243 J1263 Ca 0.2493 0.1801 0.2493 0.24239 0.16293 0.24239 0.23783 0.23832

Confidence Intervals given Road Speed alpha at 90% pg - 1 pg - 2 pg - 3 pj - 1 pj - 2 pj - 3 pj -4 pj - 5 93.9505 92.3153 93.9504 93.7169 91.8834 93.7171 93.9507 93.9504 70.3098 69.0861 70.3098 70.135 68.7629 70.1351 70.31 70.3098 46.6692 45.8569 46.6692 46.5531 45.6424 46.5532 46.6693 46.6692 23.0285 22.6277 23.0285 22 .9713 22.5219 22.9713 23.0286 23.0285 0.61212 0.60147 0.61212 0.6106 0.59866 0.6106 0.61213 0.61212 24.2528 23.8307 24.2528 24.1925 23.7192 24.1925 24.2528 24.2528 47.8934 47.0598 47.8934 47.7743 46.8397 47.7744 47.8936 47.8934 71.5341 70.289 71.53 4 71.3562 69.9602 71.3564 71.5343 71.534 95.1747 93.5182 95.1747 94.9381 93.0807 94.9383 95.175 95.1747



### Ro **ad Force Com** **par isons** 

0 200 400 600 800 1000 1200

0 20 40 60 80

**Ro ad**  **Spe ed**  **[ mp**  **h] F** **o r** **c e** **[ l** **b f** **]** pg-1 pg-2 pg-3 pj -1 pj -2 pj -3 pj -4 pj -5