Urban Turbulence and Wind Gusts for Micro Air Vehicle 

Bio-inspired Designs 

by Cheryl L. Klipp and Edward Measure 

ARL-TR-5492 March 2011 

Approved for public release; distribution unlimited. 
NOTICES 

Disclaimers 

The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents. 

Citation of manufacturer’s or trade names does not constitute an official endorsement or 

approval of the use thereof. 

Destroy this report when it is no longer needed. Do not return it to the originator. 
Army Research Laboratory 

Adelphi, MD 20783-1197 

ARL-TR-5492 March 2011 

Urban Turbulence and Wind Gusts for Micro Air Vehicle 

Bio-inspired Designs 

Cheryl L. Klipp and Edward Measure 

Computational and Information Sciences Directorate, ARL 

Approved for public release; distribution unlimited.. 
ii

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY) 

March 2011 

2. REPORT TYPE 

DRI 

3. DATES COVERED (From - To) 

4. TITLE AND SUBTITLE 

Urban Turbulence and Wind Gusts for Micro Air Vehicle Bio-inspired Designs 

5a. CONTRACT NUMBER 

5b. GRANT NUMBER 

5c. PROGRAM ELEMENT NUMBER 

6. AUTHOR(S) 

Cheryl L. Klipp and Edward Measure 

5d. PROJECT NUMBER 

FY 10CIS-07 

5e. TASK NUMBER 

5f. WORK UNIT NUMBER 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

U.S. Army Research Laboratory 

ATTN: RDRL-CIE-D 

2800 Powder Mill Road 

Adelphi, MD 20783-1197 

8. PERFORMING ORGANIZATION 

 REPORT NUMBER 

ARL-TR-5492 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 

11. SPONSOR/MONITOR'S REPORT 

 NUMBER(S) 

12. DISTRIBUTION/AVAILABILITY STATEMENT 

Approved for public release; distribution unlimited. 

13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

We discuss the effects of wind turbulence encountered in an urban street canyon on very small unmanned aerial vehicles 

(UAVs) in the context of field data from the Joint Urban 2003 Experiment in Oklahoma City, OK. We present equations for 

the aerodynamics of such a UAV and derive equations to estimate the torque and forces encountered as a function of turbulent 

changes in wind velocity. We use sonic anemometer data from the experiment to compute wind velocity changes over a 

daylong sampling period with a temporal resolution of one tenth of a second. These changes are then used to compute resulting 

forces on notional UAVs of size comparable to small birds and butterflies, and for a Wasp II UAV for comparison. 

Computations are made for three locations using data measured near the middle of the street canyon at 1.5 and 15.7 m above 

ground level (AGL), as well as at 8.0 m AGL in a nearby intersection. We show graphs of turbulent kinetic energy, maximum 

acceleration encountered, and others. We found that accelerations greater than one gravity occur frequently, especially for the

lighter vehicles, and accelerations of several gravities were common.

15. SUBJECT TERMS

Micro UAV, urban turbulence 

16. SECURITY CLASSIFICATION OF: 

17. LIMITATION 

 OF 

 ABSTRACT 

UU 

18. NUMBER 

 OF 

 PAGES 

28 

19a. NAME OF RESPONSIBLE PERSON 

Cheryl L. Klipp 

a. REPORT 

Unclassified

b. ABSTRACT 

Unclassified

c. THIS PAGE 

Unclassified 

19b. TELEPHONE NUMBER (Include area code) 

(301) 394-2543 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18 
iii

Contents 

List of Figures iv

1. Objective 1

2. Approach 1

2.1 Properties of Turbulence .................................................................................................1

2.2 Turbulence and the Micro UAV ......................................................................................2

2.3 Lift Equation....................................................................................................................3

2.4 Relative Impact of Turbulence in the Vertical and Horizontal .......................................4

2.5 Setup of Wind Field ........................................................................................................5

3. Results 6

4. Conclusions 12

5. References 14

6. Transitions 15

Appendix. Sonic Anemometer: Principle of Operation 17

List of Symbols, Abbreviations, and Acronyms 19

Distributuon List 20
iv

List of Figures 

Figure 1. (a) Ten minutes of vertical component data, 1800–1810 universal time coordinated 

(UTC) (near noon local time) of day 190, and (b) 10 s of the same data. .................................2

Figure 2. (a) PDF of 10 min of vertical component data in figure 1, 1800–1810 UTC (the red 

line is Gaussian with same mean and standard deviation as data), and (b) pdf of 

differences between adjacent data points. ..................................................................................2

Figure 3.  The locations of frozen turbulence data points being advected by the mean wind, 

UX. Aircraft will then traverse the data fields at an optimal mean wind speed UF. ...................6

Figure 4. (a) Time series of TKE in each 10-min block of data at the mid-canyon tower. 

Note that the TKE levels are lower at night than in the day, also that TKE levels are 

comparable at the two levels at night, but the higher elevation has greater TKE levels in 

the day compared to TKE levels at the lower elevation. (b) Is the same as (a) but with 

intersection data added. TKE levels in the intersection are considerably larger than at the 

mid-canyon location. ..................................................................................................................7

Figure 5. (a) Time series of number of accelerations greater than 1G in each 10-min block of 

data at the mid-canyon tower (6000 data points). At night, the lower level has more high 

G accelerations than the upper level. During the day, the situation is reversed. (b) Is the 

same as (a) but with intersection data added. The intersection has a much higher number 

of high G accelerations than any of the mid-canyon levels. All are calculated for the 

hummingbird mass/area ratio. ....................................................................................................8

Figure 6. (a) Time series of maximum acceleration in each 10-min block of data at the midcanyon tower. Note that the largest mid-canyon acceleration occurs at the 1.5 m level at 

night, and even in the daytime, larger accelerations occur at the lower level. (b) Is the 

same as (a) but with intersection data added. The intersection usually has higher 

accelerations than mid-canyon, with a few exceptions at night. All are calculated for the 

hummingbird mass/area ratio. ....................................................................................................9

Figure 7. (a) Maximum acceleration as a function of the number of accelerations greater than 

1G in each 10-min block of data at the mid-canyon tower. Note that the largest midcanyon acceleration does not correspond to the largest number of greater than 1G events. 

Also note that accelerations of 2G occur even when the number of greater than 1G events 

is relatively low. (b) Is the same as (a) but with intersection data added. All are calculated 

for the hummingbird mass/area ratio. ......................................................................................10

Figure 8. (a) Number of accelerations greater than 1G in each 10-min block of data at the 

mid-canyon tower (6000 data points) as a function of TKE for a humming bird mass/area 

ratio. TKE is a reasonable predictor of the number of accelerations greater than 1G. (b) Is 

the same as (a) but with intersection data added. .....................................................................10

Figure 9. (a) Maximum acceleration in each 10-min block of data at the mid-canyon tower 

as a function of TKE for a humming bird mass/area ratio. Note that TKE is not a good 

predictor of maximum acceleration. (b) Is the same as (a) but with intersection data 

added. .......................................................................................................................................11

 
v

Figure 10. (a) Number of accelerations greater than 1G in each 10-min block of data (6000 

data points) at the 1.5 m level of the mid-canyon tower for different aircraft types. 

Humming birds and wrens have similar mass/area ratios and therefore similar responses 

to turbulence. The possible response of the WASP II UAV is included for reference. (b) 

is the same as (a) but with butterfly data added. The much smaller mass/area ratio makes 

butterflies more susceptible to turbulence. ..............................................................................12

 
vi

INTENTIONALLY LEFT BLANK. 
1

1. Objective 

The objective of this effort is to develop a more realistic understanding of turbulence effects on 

small aircraft to aid in the design of these small vehicles, improve computer modeling of small 

scale turbulence, and ultimately produce effective decision aids for the deployment of small 

aircraft in urban settings. 

2. Approach 

2.1 Properties of Turbulence 

Turbulence is a property of the flow, not the fluid. It is heavily influenced by boundary 

conditions. There is no official definition of turbulence. Most modern textbooks just list some of 

the properties of turbulent flow (Kundu, 1990; Shivamoggi, 1998) such as the following: 

• Large fluctuations about the mean values 

• Enhanced rates of momentum, heat and mass transport 

• Multiple scales of motion 

• Without energy input, the turbulent motion decays 

Although turbulence data can be approximated (figure 1) with a Gaussian probability density 

function (pdf), in reality, there are “fat tails” with slightly more extreme values than predicted by 

a Gaussian with the same mean and standard deviation (figure 2a). Even more important than the 

slight variation from Gaussian statistics is the fact that the data are not organized in a random 

manner, at least not over short time and spatial scales (Frisch, 1995). The differences between 

closely spaced (in time or space) adjacent data points, which are important to determining the 

instantaneous forces on micro flyers, do not have a Gaussian pdf (figure 2b). Turbulent data is 

not random data but has some kind of organization. Due to the small size of the new micro 

unmanned aerial vehicles (UAVs), this organization becomes more significant than it would be 

for a larger aircraft. 

Gaussian based spectral models to simulate the wind fluctuation fields are the best option 

available to micro-system developers. These models do not capture the non-Gaussian wind 

difference. The ability to completely simulate all properties of turbulent wind fields is a current 

topic of research. Rosales and Meneveau (2006) have been able to replicate non-Gaussian wind 

differences while maintaining spectral and other properties, but fully admit that their method 

fails to replicate vortical structures. To remedy this shortcoming of computer simulated data, this 
2

report uses measured field data. Such data can provide a useful supplement and corrective to the 

known deficiencies of the simulations. 

Figure 1. (a) Ten minutes of vertical component data, 1800–1810 universal time coordinated (UTC) (near noon 

local time) of day 190, and (b) 10 s of the same data. 

Figure 2. (a) PDF of 10 min of vertical component data in figure 1, 1800–1810 UTC (the red line is Gaussian with 

same mean and standard deviation as data), and (b) pdf of differences between adjacent data points. 

2.2 Turbulence and the Micro UAV 

The micro UAV is more vulnerable to turbulence than its bigger cousins for both dynamic and 

environmental reasons. Dynamically, its smaller size and lower speed means that much smaller 

forces can significantly affect its trajectory. Environmentally, it is more vulnerable because it is 

expected to fly in the highly cluttered, turbulent atmosphere near the ground. Maneuvering in a 

-2 -1 0 1 2

100

101

102

103

-1.5 -1 -0.5 0 0.5 1 1.5

100

101

102

10 a) b) 3

Wind Speed (m/s) Wind Speed Difference (m/s) 

0 1000 2000 3000 4000 5000 6000

-1.5

-1

-0.5

0

0.5

1

1.5

2

120 140 160 180 200

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Data Index Data Index 

Wind Speed (m/s) Wind Speed (m/s) 

a) b) 
3

turbulent atmosphere cluttered with potential obstacles is thus a daunting task, but it is one that 

birds, bats, and insects routinely solve, and solve using only onboard sensors and remarkably 

slow information processing systems―processors with a cycle time one million times slower 

than that of a modern microprocessor. 

Turbulent structure on a scale comparable to its own size can yaw, pitch, and (especially) roll the 

aircraft. For a characteristic aircraft dimension of l, these tumbling forces scale like l

2 (wing area, 

for example), the resultant torques scale like l f ן ݈3

 but the moment of inertia I scales like I 

5l ݈2 ൈ  ݏݏܽܯ ן

. Consequently, as size decreases, the tendency to tumble or slew increases 

quadratically. 

Suppose that force ma corresponded to an uncompensated torque of ߬ = mab/5, where b is the 

wingspan, and further assume that the relevant moment of inertia was I = mb2/10 (compare a 

solid cylinder of diameter d at md2

/8). Then angular acceleration ߙ is given by 

ߙ ൌ  ߬/I = (mab/5)/(mb2

/10) = 2 a/b. (1) 

So for a b = 20 cm wingspan and acceleration a = G = 9.8 m/s2

, ߙ = 98 radians/s2, which if 

uncompensated for 0.1 s leads to a roll of 28°. 

Turbulent variations in wind speed and direction also result in changes in the lift force. A 

resulting linear acceleration of 1G uncompensated for 0.1 s produces a displacement of 4.9 cm. 

The displacement becomes 4.9 m if the acceleration is uncompensated for a full second. Even the 

smaller number could threaten a vehicle attempting to move through tight spaces. At the 

realistically encountered acceleration of 3G, a 5.0-cm displacement occurs in less than 60 ms. In 

sections 2.3–2.5, we have adopted a threshold of a 1G (9.8 m s–2) acceleration for the designation 

of “significant events.” 

2.3 Lift Equation 

The fundamental equation of lift (Tennekes, 2009) is 

2

2

1  L AvCL , (2) 

where L is lift, CL is the lift coefficient, ߩ is air density, A is wing area, and v is the airspeed. The 

lift coefficient CL is a complicated function of wing shape and angle of attack, but for a thin wing 

at small angles of attack 

CL  2 , (3) 

where ߠ is the angle of attack (in radians). For most flyers, natural and manmade, the optimal 

angle of attack is on the order of 6° and the airspeed is adjusted so that the total lift force 

balances the force of gravity. 
4

2.4 Relative Impact of Turbulence in the Vertical and Horizontal 

In a turbulent wind, the fluctuating components of the wind speed appear as fluctuations in the 

airspeed and angle of attack (steady winds affect the ground velocity but not the airspeed). The 

effect on lift can be summarized by 

AvdvCd C AvdL L

L      

 







  2

2

1

 (4) 

with dv as the fluctuating component of the wind. For the small angle, thin wing approximation 

for the coefficient of lift 





 2



CL . (5) 

For small angles, the angle between  dvvv 

 and is 

d |)sin(   vdvvvdvv |)||/(||            . (6) 

Maximum values of d occur when the fluctuating component is perpendicular to the main 

component and 

vdvd ||/||    . (7) 

Maximum changes in the airspeed, by contrast, occur when the velocity fluctuation is parallel to 

the air speed. Let us compare the two terms for the rather benign case where air speed = 5 m/s 

and the fluctuating wind component is dv  0.2 m/s. From the vertical component data in figure 

1, this is seen to be reasonable. Then the maximum value of d  04.0 . 

A normal cruising speed value of the angle of attack is about 0.11 (in radians), so a fluctuation of 

that magnitude (݀ߠ ൌ 0.04ሻ in the perpendicular direction would represent a 36% fluctuation in 

lift, dL/L. For a parallel component of the same magnitude, we have the following: 

%.8

25

22

2  

 



  v

vdv

L

dL

 (8) 

The modest turbulence in our example is enough to drastically affect the trajectory of the aircraft. 

The 36% lift change cited, for example, would produce a significant velocity change. 

Such errors are much too large for remotely controlled flight through a complicated airspace of 

trees, branches, and window openings. It is quite clear that autonomous real-time sensing and 

control are needed for such maneuvers. 

 
5

The fundamental physics of flight dictates that an aircraft support itself against gravity by 

transferring downward momentum to air at a rate dp/dt = mg. At cruising speed V, and optimal 

angle of attack, wing area A and lift L (and consequently aircraft weight mg) are related 

approximately as 

L = mg = 0.4 V2 A. (9) 

For flapping flight, this requires adjustment for the fact that lift takes place only on the down 

stroke and also for unsteady aerodynamic effects, which permit higher angles of attack and 

consequently smaller wings (Sane, 2003). Analyses in the current report are confined to fixedwing craft, but the effects of turbulence are similar when the above differences are allowed for. 

The more complex aspects of flapping flight, and its advantages for small flyers, are deferred to 

later work. 

2.5 Setup of Wind Field 

To calculate the effects of turbulence on a small aircraft, we first need to set up a turbulent wind 

field for the aircraft to traverse. Wind field simulator software algorithms are very sophisticated 

but are fundamentally stochastic, whereas turbulent data over short distances/small time scales 

are not stochastic (Frisch, 1995). So instead of using a simulated wind field, we use a constructed 

wind field using data taken from a street canyon and intersection in Oklahoma City, OK, as part 

of the Joint Urban 2003 (JU2003) Defense Threat Reduction Agency (DTRA) and Department 

of Homeland Security (DHS) funded field campaign (Allwine and Flaherty, 2006). The data are 

the three components of the wind vector measured at a rate of 10 times per second with sonic 

anemometers deployed at a variety of locations within the Park Avenue street canyon (see the 

appendix for details of the sonic anemometer). 

The day of year 190, corresponding to 9 July 2003, was chosen for its fairly typical and steady 

properties. Upwind of the urban center, 30 m above ground level, the mean wind speed for the 

day was 6.6 m/s, with slightly slower winds at night, slightly faster during the day. The mean 

wind direction was 192° ± 10°. This is roughly at right angles to the east-west oriented Park 

Avenue street canyon axis, but winds in the canyon were channeled along the canyon axis. For 

this day sunrise was at 11:20 UTC, solar noon at 18:35 UTC, and sunset at 1:50 UTC (from the 

National Oceanic and Atmospheric Administration (NOAA) online solar calculator). 

The three-dimensional wind vector data from a fixed anemometer are used to establish a spatially 

distributed wind field through the application of Taylor’s frozen turbulence hypothesis (Frisch, 

1995; Kaimal and Finnigan, 1994), which makes the assumption that the turbulent part of the 

wind field is evolving at a sufficiently slow rate compared to the mean wind speed that one can 

visualize the turbulent wind field as being frozen as it is advected past the anemometer by the 

mean wind velocity. 

The dots in figure 3 represent the location of “frozen turbulence” data points moving with the 

wind. The points are irregularly spaced due to turbulent variability in wind speed, UX. The time 
6

between points is fixed, in this case at 0.1 s, so the spacing between adjacent points, i and i–1, is 

the mean wind speed between the two points multiplied by 0.1 s: ∆ݔ ௜ൌ ሺݑ௫௜ ൅ ݑ௫௜ିଵ/2ሻ∆ݐ. 

Typical scales for ∆ݔ ௜are 10–20 cm at mid-canyon and 20–40 cm in the intersection. These are 

comparable to the scale of small aircraft. When the aircraft traverses this field at its optimal 

airspeed, UF, the spatial scales translate into temporal scales of 7–35 ms at the mid-canyon 

location and 13–52 ms in the intersection. Human remote control is unlikely to be able to react 

quickly enough to compensate for turbulence. 

Figure 3. The locations of frozen turbulence data points being advected by the mean wind, UX. Aircraft will then 

traverse the data fields at an optimal mean wind speed UF.

The data at each point is the deviation at that point from the mean vertical and along-canyon 

wind vector components. This is added to the optimal airspeed vector UF to create the wind field. 

The combination of airspeed and mean wind speed make up the ground speed of the aircraft. 

Since the details of how quickly an aircraft can react to and recover from turbulence induced 

changes in lift will vary with the engineering details of each aircraft, we have made the 

simplifying assumption that steady level flight is attained between each wind field point. 

The resulting wind field data at each point are plugged into the lift equation, equations 2 and 3, 

to obtain a lift force at each data point. Assuming that steady level flight was attained at the 

previous point, the difference in lift from one point to the next is the net force on the aircraft 

between the two data points. With F = (Li – Li-1), the acceleration is a = F/m, where m is the mass 

of the aircraft. For most of this analysis the mass used is 3 g and a wing area of 12 cm2

, 

comparable to a hummingbird as well as some of the small aircraft under development. It is 

assumed that the aircraft is flying parallel to the canyon axis. Secondary mean flows and 

turbulence in the cross-canyon direction are not accounted for. 

3. Results 

Turbulence kinetic energy (TKE) is a common measure of the strength of turbulence. Figure 4 

shows time series of TKE for the three locations analyzed in this report, 1.5 and 15.7 m above 

street level at a mid-canyon location 8 m from the south side of the canyon, and at 8.0 m above 

Ux

UF

uxi uxi-1

Δxi
7

street level at the southeast corner of the intersection to the east of the canyon. As is typical of 

the atmosphere, daytime turbulence levels are higher than nighttime levels (local noon is at 1830 

UTC). Also typical of urban turbulence, levels of TKE are higher in the intersections than inside 

the urban canyon (Nelson et al., 2007; Ramamurthy et al., 2007; Roth, 2000; Grimmond et al., 

1998; Rotach, 1995). 

Figure 4. (a) Time series of TKE in each 10-min block of data at the mid-canyon tower. Note that the TKE levels 

are lower at night than in the day, also that TKE levels are comparable at the two levels at night, but the 

higher elevation has greater TKE levels in the day compared to TKE levels at the lower elevation. (b) Is 

the same as (a) but with intersection data added. TKE levels in the intersection are considerably larger 

than at the mid-canyon location.

As discussed in section 2.2, a threshold acceleration of 1G was chosen as a metric to categorize 

the effects of turbulence on small aircraft. Figure 5 is the time series of the number of times the 

acceleration exceeded 1G in each 10-min block of data. At night, the lower elevation sonic, 

1.5 m, encounters more high G accelerations than the upper level sonic, 15.7 m. During the day, 

the situation is reversed. It is not yet known if this is true in general or just for this case. As 

might be expected, times and locations with higher TKE levels encounter significant events more 

often than lower TKE times. The intersection has a much higher number of high G accelerations 

than any of the mid-canyon levels. These events are calculated using a hummingbird mass to 

wing area ratio. 

0 5 10 15 20

0

0.5

1

1.5

2 1.5 m, midcanyon

15.7 m, midcanyon

0 5 10 15 20

0

1

2

3

4

5

6

7

8

1.5 m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

Time of Day 190 (UTC) Time of Day 190 (UTC) 

TKE (m2/s2) 

a) b) TKE (m2/s2) 
8

Figure 5. (a) Time series of number of accelerations greater than 1G in each 10-min block of data at the mid-canyon 

tower (6000 data points). At night, the lower level has more high G accelerations than the upper level. 

During the day, the situation is reversed. (b) Is the same as (a) but with intersection data added. The 

intersection has a much higher number of high G accelerations than any of the mid-canyon levels. All are 

calculated for the hummingbird mass/area ratio.

Another useful metric to determine effects of turbulence on small aircraft is the maximum 

acceleration encountered in a block of time (10 min) plotted in figure 6. The TKE–maximum 

acceleration correlation is less clear than the correlation between TKE and fraction of significant 

events. Although the intersection location encounters larger maximum values than the canyon 

location, the difference is not as large as might be expected based solely on TKE values 

(figure 4b). The largest mid-canyon acceleration occurs at the 1.5-m elevation at night, and even 

in the daytime, larger accelerations can occur at the lower elevation, also an indication that TKE 

is not the only factor. 

0 5 10 15 20

0

50

100

150

200

250

300

350

1.5 m, midcanyon

15.7 m, midcanyon

0 5 10 15 20

0

100

200

300

400

500

600

700

800

900

1000

1.5 m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

Time of Day 190 (UTC) Time of Day 190 (UTC) 

Number of accelerations > 1G 

a) b) Number of accelerations > 1G 
9

Figure 6. (a) Time series of maximum acceleration in each 10-min block of data at the mid-canyon tower. Note 

that the largest mid-canyon acceleration occurs at the 1.5 m level at night, and even in the daytime, larger 

accelerations occur at the lower level. (b) Is the same as (a) but with intersection data added. The 

intersection usually has higher accelerations than mid-canyon, with a few exceptions at night. All are 

calculated for the hummingbird mass/area ratio.

The scatter plots in figure 7 of the maximum acceleration in a 10-min block as a function of the 

number of significant events in the same block show that the number of greater than 1G events in 

a 10-min block is not a good predictor of the maximum acceleration in that block. Comparing the 

number of significant events to the TKE in each block of data shows that TKE is a fairly good 

predictor of the number of accelerations greater than 1G (figure 8), while plots of the maximum 

acceleration as a function of TKE show that TKE is a poor predictor of the maximum 

acceleration (figure 9).

Time of Day 190 (UTC) Time of Day 190 (UTC) 

Maximum Acceleration (G) 

Maximum Acceleration (G) 

0 5 10 15 20

0

1

2

3

4

5

6

7

8

9

1.5 m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

0 5 10 15 20

0

1

2

3

4

5

6

7

1.5 m, midcanyon

15.7 m, midcanyon

a) b) 
10

Figure 7. (a) Maximum acceleration as a function of the number of accelerations greater than 1G in each 10-min 

block of data at the mid-canyon tower. Note that the largest mid-canyon acceleration does not 

correspond to the largest number of greater than 1G events. Also note that accelerations of 2G occur 

even when the number of greater than 1G events is relatively low. (b) Is the same as (a) but with 

intersection data added. All are calculated for the hummingbird mass/area ratio.

Figure 8. (a) Number of accelerations greater than 1G in each 10-min block of data at the mid-canyon tower (6000 

data points) as a function of TKE for a humming bird mass/area ratio. TKE is a reasonable predictor of 

the number of accelerations greater than 1G. (b) Is the same as (a) but with intersection data added.

0 0.5 1 1.5 2 2.5

0

50

100

150

200

250

300

350

400

1.5m, midcanyon

15.7 m, midcanyon

0 2 4 6 8

0

200

400

600

800

1000

1200

1.5m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

TKE (m2/s2) 

a) b) 

Number of accelerations > 1G Number of accelerations > 1G 

TKE (m2/s2) 

0 50 100 150 200 250 300 350

0

1

2

3

4

5

6

7

1.5 m, midcanyon

15.7 m, midcanyon

0 200 400 600 800 1000

0

1

2

3

4

5

6

7

8

9

1.5 m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

Number of accelerations > 1G 

Maximum Acceleration (G) 

a) b) Maximum Acceleration (G) 

Number of accelerations > 1G 
11

Figure 9. (a) Maximum acceleration in each 10-min block of data at the mid-canyon tower as a function of TKE 

for a humming bird mass/area ratio. Note that TKE is not a good predictor of maximum acceleration. 

(b) Is the same as (a) but with intersection data added.

Given equations 2, 3, and 9, the ratio of mass to wing area determines the accelerations 

generated by the wind data. This ratio is also called wing loading. The hummingbird and wren 

have similar ratios and therefore have similar accelerations (figure 10). The butterfly, having a 

small mass and relatively large wing area, feels the impact of the turbulence as a significantly 

larger number of significant events. The results for the mass to wing area ratio of the fielded 

WASP II UAV are shown for comparison, however, its physical size is too large for this analysis 

to be realistic. The wing loading is about 2.5 kg/m2 for a hummingbird, 2.2 kg/m2 for a wren, 

0.2 kg/m2

 for a butterfly, and 6.0 kg/m2 for the WASP II UAV. For comparison, the wing 

loading for many commercial airliners is in the range of 650–800 kg/m2. 

 

0 0.5 1 1.5 2

0

1

2

3

4

5

6

7

1.5 m, midcanyon

15.7 m, midcanyon

0 2 4 6 8

0

1

2

3

4

5

6

7

8

9

1.5 m, midcanyon

15.7 m, midcanyon

8.0 m, intersection

TKE (m2/s2) 

a) b) 

Maximum Acceleration (G) 

TKE (m2/s2) 

Maximum Acceleration (G) 
12

Figure 10. (a) Number of accelerations greater than 1G in each 10-min block of data (6000 data points) at the 

1.5 m level of the mid-canyon tower for different aircraft types. Humming birds and wrens have similar 

mass/area ratios and therefore similar responses to turbulence. The possible response of the WASP II 

UAV is included for reference. (b) is the same as (a) but with butterfly data added. The much smaller 

mass/area ratio makes butterflies more susceptible to turbulence.

4. Conclusions 

This work used actual measured urban turbulence data to compute resultant accelerations of 

several small aircraft with a simplified model of flight dynamics. The analysis carried out in this 

effort has several limitations that suggest the desirability of a more complete and detailed 

analysis. Our data set, though one of the most extensive in existence, samples just one city 

during one month and has no high wind events, strongly hinting that far more severe effects are 

likely. Also, because the data set was taken at 10 samples per second, smaller scale turbulent 

events are not resolvable, with the smallest measurable structures in this data set being rather 

larger than the smallest UAV. Finally, the concentration of our analysis on the number of events 

exceeding our threshold of 1G acceleration and the maximum acceleration provides only two 

metrics for effects that ultimately need full aerodynamic simulations to characterize. 

Several compelling findings have come out of this analysis, in spite of its limitations. One is that 

turbulence intermittency is significant at scales on the order of tens of centimeters in urban 

turbulence. Some schools of thought consider turbulence intermittency to be significant only at 

scales comparable to or smaller than the Kolmogorov dissipation scale, which is on the order of 

millimeters for atmospheric flows. Given the 10-cm transducer separation and the data rate of 

10 per second, translating to spatial rates of tens of centimeters, the data from these sonic 

anemometers are too coarse to show dissipation scale phenomena, and therefore not expected to 

0 5 10 15 20

0

50

100

150

200

250

Hummingbird

Wren

WASPII UAV

0 5 10 15 20

0

500

1000

1500

2000

2500 Hummingbird

Wren

WASPII UAV

Butterfly

Time of Day 190 (UTC) Time of Day 190 (UTC) 

a) b) 

Number of accelerations > 1G 

Number of accelerations > 1G 
13

resolve intermittency phenomena. These sonics are able to resolve inertial scales that start at 

about 1 Hz in the atmosphere and extend beyond the Nyquist frequency (5 Hz for the data used 

here). Some researchers have found intermittency to be observable at inertial scales, but 

intermittency at inertial scales is inconsistent with Kolmogorov turbulence theory, making 

intermittency at inertial scales unpalatable. 

Another significant finding is that the primary influence of turbulence at this scale is in changes 

in the angle of attack in the lift equation rather than the speeding up or slowing down of the wind 

in the direction of flight. Since it is possible that the nature of turbulent fluctuations above the 

atmospheric boundary layer are quite different than the street level turbulence studied here, it is 

not known if these findings scale up to commercial air traffic. 

Another conclusion is that human remote control is unable to react quickly enough to the effects 

of turbulence. This makes it necessary for turbulence control to be onboard and autonomous 

whether or not overall flight control is remote or autonomous. 

Also unique to this work is the manner in which field data are used as a turbulent wind field for 

modeling effects on aircraft. Typically, computer simulated turbulence fields are used by the 

design community. Since the computer generated fields do not reproduce intermittency, we have 

devised a manner in which field data can be used instead. This method produces more realistic 

wind fields than the simulated fields, but to obtain the more closely spaced data more appropriate 

for nano-UAVs, an instrument other than a sonic anemometer will be needed. 
14

5. References 

Allwine, K. J.; Flaherty, J. E. Joint Urban 2003: Study Overview and Instrument Locations; 

PNNL-15967; Pacific Northwest National Laboratory: Richland, WA, 2006. 

Frisch, U. Turbulence: The Legacy of A. N. Kolmogorov, Cambridge University Press: New 

York, NY, 1995, pp. 296. 

Grimmond, C.S.B.; King, T. S.; Roth, M.; Oke, T. R. Aerodynamic Roughness of Urban Areas 

Derived from Wind Observations. Boundary-Layer Met. 1998, 98, 1–24. 

Heinemann, Detlev; Langner, Dirk; Stabe, Ulf; Waldi, Hans-Peter. Measurement and correction 

of ultrasonic anemometer errors and impact on turbulence measurements, 1997 

http://www.energiemeteorologie.de/publications/wind/conference/1997/Measurement_and_

Correction_of_Ultrasonic_Anemometer_Errors_and_impact_on_turbulence_measurements.p

df (accessed March 2011). 

Kaimal, J. C.; Finnigan, J. J. Atmospheric Boundary Layer Flows, Oxford University Press, 

1994, pp. 289. 

Kundu, P. K. Fluid Mechanics, Academic Press, Inc.: San Diego, CA, 1990, pp. 638. 

Nelson, M. A.; Pardyjak, E. R.; Klewicki, J. C.; Pol, S. U.; Brown, M. J. Properties of the Wind 

Field Within the Oklahoma City Park Avenue Street Canyon, Part I: Mean Flow and 

Turbulence statistics. J. of Applied Meteorology and Climatology 2007, 46, 2038–2054. 

Ramamurthy, P.; Pardyjak, E. R.; Klewicki, J. C. Observations of the Effects of Atmospheric 

Stability on Turbulence Statistics Deep Within an Urban Street Canyon. J. of Applied 

Meteorology and Climatology 2007, 46, 2074–2085. 

Rosales, C.; Meneveau, C. A Minimal Multiscale Lagrangian Map Approach to Synthesize 

Non-Gaussian Turbulent Vector Fields. Physics of Fluids 2006, 18, 075104 

Rotach, M. W. Profiles of Turbulence Statistics In and Above an Urban Street Canyon. 

Atmospheric Environment 1995, 29, 1473–1486. 

Roth, M. Review of Atmospheric Turbulence Over Cities. Q. J. R. Meteorol. Soc. 2000, 126, 

941–990. 

Sane, Sanjay P. The Aerodynamics of Insect Flight. J. of Experimental Biology 2006, 206, 

4191–4208. 

Shivamoggi, B. K. Theoretical Fluid Dynamics, 2nd ed.; John Wiley and Sons: NewYork, NY, 

1998, pp. 555. 

Tennekes, H. The Simple Science of Flight: From Insects to Jumbo Jets, rev. ed., MIT Press, 

2009, pp. 176. 
15

6. Transitions 

This work will transition into the U.S. Army Research Laboratory (ARL) program for 

biologically inspired approaches to environmental awareness and control of small unmanned 

aerial systems (UASs) in turban environments. In conjunction with this Director’s Research 

Initiative (DRI), we delivered some preliminary results to Dr. J. Sean Humbert, Assistant 

Professor at University of Maryland and director of the Autonomous Vehicle Laboratory, to 

inform his group of the non-Gaussian nature of turbulent fluctuations as they might impact their 

robotic micro flyer design program. The present work will be of interest to Professor Inderjit 

Chopra and several graduate students from the University of Maryland’s Department of 

Aerospace Engineering as well. The present full report will be forwarded as a follow-up to those 

previous interactions. In addition, the work performed here will be of interest to micro flyer 

designers and those who are planning for the future use of micro sensors on micro flyers for 

urban surveillance missions inside and outside of buildings. Furthermore, Dr. Klipp will get in 

contact with Mr. Mark Bundy of the Vehicle Test Directorate (VTD) in the design and setup of a 

micro flyer test facility being put together by VTD near Aberdeen Proving Ground (APG), MD, 

to discuss characterization of turbulence in their test facility using a sonic anemometer to help 

confirm future work. Dr. Measure will discuss the work with his SBIR Phase II contractors 

developing biomimetic navigation for small and micro UAV. 

Follow-on research should address inclusion of the cross wind turbulence component and 

secondary higher order fluctuation effects to complete the picture of time dependent forces on 

micro flyers in urban domains. 

 
16

INTENTIONALLY LEFT BLANK. 

 
17

Appendix. Sonic Anemometer: Principle of Operation 

Sound waves in air are carried with the wind, so that a sound wave going downwind covers 

ground faster than one headed in the opposite direction. That fact forms the basis for the 

operation of the sonic (or ultrasonic) anemometers that were used for the measurements 

discussed here. Sonic anemometers usually have paired transducers that transmit sound pulses 

forward and back, measuring the travel time in each case. 

Kaimal and Finnigan (1994) discuss the principle of operation of the sonic anemometer and 

thermometer in their book Atmospheric Boundary Layer Flows (pp. 247–249). Much of the 

discussion below is adapted from theirs, and from Heinemann et al. (1997). 

If A and B are transducers located a distance d apart, and the component of wind in the direction 

from A to B is v, then the transit time from A to B is 

 tAB = d/(c + Vd), (A-1) 

while the transit time in the opposite direction is 

 tBA = d/(c - Vd), (A-2) 

where c is the speed of sound in air and Vd is the along path component of the wind velocity. The 

transit time measurements permit computation of Vd and c. We know c approximately, of course, 

but it does vary, being proportional to the square root of the virtual temperature, so the virtual 

temperature can also be inferred. In the ideal gas approximation, the equation for the velocity of 

sound in air is 

M

RT

csound

  , (A-3) 

where CC vp   / = the adiabatic constant; Cp and Cv are the specific heats at constant pressure 

and constant volume, respectively; R is the universal gas constant; T is absolute temperature; and 

M is the average molecular weight of the gas. 

Consequently, T can be inferred from the speed of sound to be 

./ 2  sound RMcT (A-4) 

Since the average molecular weight of air varies with humidity, it is usually more convenient to 

just use the molecular weight of dry air, M dry in which case we get the virtual temperature Tv

./ 2

v  sounddry RcMT (A-5) 
18

Typical sonic anemometers have either two or three mutually orthogonal such pairs of 

transducers permitting two- or three-dimensional measurements of the wind. All the data 

considered in this report were taken with three-dimensional sonic anemometers. Numerous 

effects combine to limit the precision, accuracy, and time resolution with which the winds can be 

measured, many of which are discussed in Kaimal and Finnigan (1994). 

 
19

List of Symbols, Abbreviations, and Acronyms 

APG Aberdeen Proving Ground 

ARL U.S. Army Research Laboratory 

DHS Department of Homeland Security 

DRI Director’s Research Initiative 

DTRA Defense Threat Reduction Agency 

JU2003 Joint Urban 2003 

NOAA National Oceanic and Atmospheric Administration 

Pdf probability density function 

TKE turbulence kinetic energy 

UAS unmanned aerial system 

UAVs unmanned aerial vehicles 

UTC universal time coordinated 

VTD Vehicle Test Directorate 
20

No of.

Copies Organization

1 ADMNSTR 

(PDF DEFNS TECHL INFO CTR 

ONLY) ATTN DTIC OCP 

 8725 JOHN J KINGMAN RD STE 0944 

 FT BELVOIR VA 22060-6218 

1 HC US ARMY RSRCH LAB 

 ATTN RDRL CIM G T LANDFRIED 

 BLDG 4600 

 ABERDEEN PROVING GROUND MD 21005-5066 

3 HCS US ARMY RSRCH LAB 

 ATTN IMNE ALC HRR MAIL & RECORDS MGMT 

 ATTN RDRL CIM L TECHL LIB 

 ATTN RDRL CIM P TECHL PUB 

 ADELPHI MD 20783-1197 

3 HCS US ARMY RSRCH LAB 

1CD ATTN RDRL CIE D C KLIPP (1 CD, 1 HC) 

 ATTN RDRL CIE S CHIEF 

 ATTN RDRL CIE S A WETMORE 

ADELPHI MD 20783-1197 

3 HCS US ARMY RSRCH LAB 

 ATTN RDRL CIE BE DIVISION 

 ADELPHI MD 20783-1197 

3 HCS US ARMY RSRCH LAB 

1CD ATTN RDRL CIE D E MEASURE (1 CD, 1 HC) 

ATTN RDRL CIE D D HOOCK 

ATTN RDRL CIE M D KNAPP 

WSMR NM 88002 

1 HC US ARMY RSRCH LAB 

RDRL-VTA C KRONINGER 

APG BLDG 1120A 

 ABERDEEN PROVING GROUND MD 21005-5066 

1 HC US ARMY RSRCH LAB 

 RDRL-SER-L B PIEKARSKI 

 ADELPHI MD 20783-1197 

1 HC US ARMY RSRCH LAB 

 RDRL-SER-L G SMITH 

 ADELPHI MD 20783-1197 

1 HC US ARMY RSRCH LAB 

 RDRL-SER-L R POLCAWICH 

 ADELPHI MD 20783-1197 

TOTAL: 20 (1 ELEC, 2 CDS, 17 HCS)