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, conversion from J1263................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 Recommendations........................................Page 12

Appendix A.........................................................Page 14

Appendix B.........................................................Page 17

Appendix D.........................................................Page 19

Appendix E.........................................................Page 21
3

Background

The US EPA has regulated Light Duty vehicle emissions and fuel economy since the 

1970’s with verification procedures in place requiring methods of road force 

measurements in order to set the emissions dynamometer absorber loading. The practical 

approach adopted to initialize the dynamometer load determination was the track 

coastdown method, which relies on vehicle deceleration as the primary indicator of road

force resistance. Over the years various improvements in the coastdown procedure and 

analyses have evolved, particularly thanks to F. T. Buckley, who introduced on-board 

anemometry with inventive instrument calibration and data reduction methods (ABCDAn Improved Coast Down Test and Analysis Method, SAE paper 950626). With the 

advent of Heavy Duty vehicle emissions regulations consideration of state-of-the-art road

force procedures unique to Heavy Duty operation is now desirable.

Objective

Our purpose will be to institute a coast down procedure able to meaningfully assess 

aerodynamic and mechanical drag associated with Heavy Duty tractor/trailer 

configurations and design feature devices. Ultimately these assessments encourage 

technical 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 aerodynamic 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

Based on theoretical simulations and utilizing concepts and assumptions contained 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 forces on several configurations. Class 8 results obtained by EPA are 

more problematic and are discussed for resolution.
5

Analysis a)...Support for J2263, conversion 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 converts 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 of 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 run, the data should be retained, in order not to compromise 

dynamometer coastdown results, if those are necessary to finalize the process. 

If the test plan uses several passes 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

 Diminish 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 offset angle may be in fact more accurate than by 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

measures true wind speed and direction:

wind sin 

(attack)

attack

 wind cos(attack) wind

 

Vair

Vroad attack

yaw off wind Vroad

yaw true

 yaw off

yaw 

true

Definitions for Model

Va: 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

 = (Vr

2

+ 2 w cos()*Vr + w2) Cal eq 1

tan(t ) = w sin() /[Vr + 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 solution matrix follows:

The summation of incremental errors squared for “i” observations is 

2

1

i

n

i

 



= 

n

i 1

[

2

Vai

2

 - (Vri

2

+ 2 w cos()*Vri + w2)]2

Setting the partial derivatives of the error-squared to zeros...

/

2

2

1

i

n

i

 



= 

n

i 1

2 [

2

Vai

2

 - (Vri

2

+ 2 w cos()*Vri + w2)]1* Vai

2

 = 0

/[-2 w cos()]

2

1

i

n

i

 



= 

n

i 1

2 [

2

Vai

2

 - (Vri

2

+ 2 w cos()*Vri + w2)]1* Vri = 0

/[-w

2

]

2

1

i

n

i

 



= 

n

i 1

2 [

2

Vai

2

 - (Vri

2

+ 2 w cos()*Vri + w2)]1* 1 = 0

In matrix form this appears as...



n

i 1

Va

2 

n

i 1

Vr 

n

i 1

1 

2 

n

i 1

Vr

2



n

i 1

Va

2 Vr 

n

i 1

Vr

2 

n

i 1

Vr -2 w cos() = 

n

i 1

Vr

3



n

i 1

Va

4 

n

i 1

Va

2 Vr 

n

i 1

Va

2

-w

2 

n

i 1

Va

2 Vr2
9

...and reduces to:

1 0 0 

2 = X1

0 1 0 -2 w cos() = X2

0 0 1 -w

2 = 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 portion can be solved by Cal eq 2 

and Cal eq3 i.e.



n

i 1

tan(t )i = 

n

i 1

w sin() /[Vri + w cos()]

tan(0) = [

n

i 1

tan(t ) i -

n

i 1

tan(m ) i] / 

n

i 1

[1 + tan(t )itan(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 by 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 coefficients 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 session 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 analysis 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 + Ca Vair

2

 

Method “pg2” is same as “pg1” except for the force model:

Force = Am + Bm Vroad + Ca Vair

2

 

Method “pg3” is same as “pg1” except for the force model:

Force = Am + Bm Vroad + Cm Vroad 

2

+ Ca Vair

2

 

Method “pj1” 

a) uses the calibration method as described in Analysis d) 

b) the force model used is

Force = Am + Ca Vair

2

 (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 + Bm Vroad + Ca Vair

2

 (1 + P yaw2) cos (yaw) 

Method “pj3” is same as “pj1” except for the force model:

Force = Am + Bm Vroad + Cm Vroad 

2

+Ca Vair

2

 (1 + P yaw2) cos (yaw) 

Method “pj4” is same as “pj3” except the force model does not use the yaw coefficient 

“P”:

Force = Am + Bm Vroad + Cm Vroad 

2

+Ca Vair

2

 cos (yaw) 
11

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

Force = Am + Bm Vroad + Cm Vroad 

2

+Ca Vair

2

 

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 statistics 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 only 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 always 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 smaller vehicles typically show Beta around 1.05. The 

Class 8 “pg” models are producing considerably less than that value, and “pj” 

models produce higher. At best, when certain subsets 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 mentioned 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 significance 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 occur 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 expected 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 Recommendations

Given that to date some difficulty persists with the Class 8 analysis 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 calibration 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 + Ca Vair

2

 . 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

Applications 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 force “F” acting 

on it against direction of motion, which is directly measurable by 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 road 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:

Fi = a + c (Vi + w) 2i referring to the ith observation; Fi,Vi are known; a, c, w unknown

Expanded

a + c Vi

2 + 2cwVi + cw2

- Fi = 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 associated with every observation. In this case the Method of Least Squares will 

find the best a, c, and w which minimizes the summation of 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 these

3 solution equations.

d/dc

2

1

i

n

i

 



= 2

i

n

i

 

1

Vi

2 

= 

n

i 1

FiVi

2

– c Vi

4

-2cwVi

3

-(a+ cw2) Vi

2 = 0

d/d(2cw) 

2

1

i

n

i

 



= 2

i

n

i

 

1

Vi = 

n

i 1

FiVi – 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

Fi – 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

Fi



n

i 1

Vi

3

+

n

i 1

Vi

2

+

n

i 1

Vi = 

n

i 1

FiVi



n

i 1

Vi

4

+

n

i 1

Vi

3

+

n

i 1

Vi

2 

= 

n

i 1

FiVi

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 by “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

fi with continuous 



vi

vf

f (V )dV (as if infinite and perfect 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 by 

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) ]2dV

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 Vf

influences the answer (and that makes sense). This convention of notation is Vj = (Vi

j 

–

Vf

j

) / j to describe the quantity from integration expressions with limits.

Jumping ahead:

A V1 + C V3 = a V1 + b V2 + c V3

A V3 + C V5 = a V3 + b V4 + c V5

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 dyno 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 aerodynamic 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 analysis is shown below: 

Model: Force= mass * dV/dt= A +C*(V+w)2

Solution for the differential equation 

of motion:

t= mass / 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 (mass)= 100 >>These are given

t v mid v m dvdt (mid v + w)2(mid v + w)4(mid v + w)2*m dvdt

time

road 

speed

avg spd t to 

t+2 force

0 60.00 58.75 -124.52 4727.22 22346589.76 -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 3339.05 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 -12038.46

82 7.77

sums> -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.

Wind Any -10 10 combined 10 -10

Count Any 41 41 82 25 17

Data speed selection:

Range 1 from Any 60 60 60 60 40

Range 1 to Any 21 8 combined 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 Va

2

(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

Wind 6.093293 mph 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 410.5905 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 1230.685 1283.985 1137.037 1239.262

Cal 

strategy> Use end of run 4, beginning of 5 Only use 40-60 mph
20

-0.11041

Wind 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 Run 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 0.383092 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

20 515.9523 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 1133.788 1170.803 1155.915

70 1322.068 1253.36 1305.113 1379.827 1439.284 1389.372

Forces Obtained With Unique Cals

0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80

Velocity [mph]

F

orc

e [lbf]

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, force 

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 60 20 -1

8 1 40 20 1 60 20 -1

9 1 60 40 1 60 20 1

10 1 60 20 -1

When a run # is selected for pg cal, the first ten data points are used for the yawoffset

yawoffset 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

Wind 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 317.284 465.943 317.285 317.249 465.957 317.232 317.315 317.285

Bm ------------

-

8.58774

-5.5E05 -----------

8.59788 0.00108 0.00105

-5.5E05

Cm ------------ ----------

-1.3E06 ---------- -----------1.3E06 -1.3E-06-1.3E06

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

20 372.364 395.305 372.364 366.245 383.852 366.244 366.444 366.331
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 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 9.58754 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

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80

Road Speed [mph]

Force [lbf]

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

Wind 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 ---------- ----------

-3.3E07 -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

30 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 9.19125 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

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80

Road Speed [mph]

Force [lbf]

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

Beta 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

Wind speed ------------ ---------- ---------- 13.7271 13.7271 13.7271 13.7271 13.7271

Yaw offset 

deg -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

-4.8E05 -----------

3.55546 0.00353 0.0017

-4.8E05

Cm ------------ ----------

-1.4E06 ---------- -----------3.4E07 -1.4E-06-1.4E06
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 0.4048

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

35 478.88 473.697 478.88 407.704 402.349 407.71 447.955 447.693

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

50 699.822 730.647 699.822 572.635 573.394 572.636 636.503 636.176

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 8.99121 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

Road Force Comparisons

0

200

400

600

800

1000

1200

0 20 40 60 80

Road Speed [mph]

Force [lbf]

pg-1

pg-2

pg-3

pj-1

pj-2

pj-3

pj-4

pj-5

#4 Same Cal pair measured over 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

Wind 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

-4.8E05 -----------

2.11032 0.0026 0.00111

-4.8E05

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 0.42694 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

30 415.538 407.251 415.538 381.664 379.649 381.667 401.232 401.059

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

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80

Road Speed [mph]

F

orc

e [lbf]

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

Wind 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

-4.8E05 -----------

9.74853 0.00135 0.00088

-4.8E05
29

Cm ------------ ----------

-1.4E06 ---------- -----------1.3E06 -1.4E-06-1.4E06

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 20.1067 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 3.28666 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 26.7699 26.6841 26.4086 26.6842 26.77 26.7699
30

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80

Road Speed [mph]

F

orc

e [lbf]

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

Wind 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 317.284 465.943 317.285 318.351 465.946 318.341 317.417 317.285

Bm ------------

-

8.58774

-5.5E05 -----------

8.59097 0.0007 0.00073

-5.5E05

Cm ------------ ----------

-1.3E06 ---------- -----------1.3E06 -1.3E-06-1.3E06
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

40 536.535 524.94 536.535 520.606 493.497 520.609 519.61 519.445

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 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 9.58698 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

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80

Road Speed [mph]

F

orc

e [lbf]

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 Direction

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

Wind 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

-5.5E05 -----------

8.52458 0.0008 0.00039 -5.5E-05

Cm ------------ ----------

-1.3E06 ---------- -----------1.3E06 -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 0.3256 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

50 656.87 659.978 656.87 627.912 621.337 627.926 642.314 641.906

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 Ca 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 6.87269 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 3.98673 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 12.1313
34

Road Force Comparisons

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80

Road Speed [mph]

F

orc

e [lbf]

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 ------------ ---------- ---------- 78.6881 78.6881 78.6881 78.6881 78.6881

Wind 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

-6.1E05 ---------- -19.2275 0.00119 0.00078-6.1E05

Cm ------------ ------------

-1.7E06 ------------ -------------1.8E06 -1.7E-06-1.7E06
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

20 223.963 398.433 223.964 205.917 384.091 205.913 220.482 219.569

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 1021.73 963.193 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 71.534 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

Road Force Comparisons

0

200

400

600

800

1000

1200

0 20 40 60 80

Road Speed [mph]

F

orc

e [lbf]

pg-1

pg-2

pg-3

pj-1

pj-2

pj-3

pj-4

pj-5