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

Table of Contents

Background………………………..…………………….…Page
3

Objective……………………………………………..….…Pag
e 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

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 (ABCD- An 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…

…measuring road force (agents which impede vehicle forward motion) at
varying speeds

…separation of aerodynamic and mechanical losses (desirable, may not
be essential)

…provision of relevant statistics to establish the levels of
measurement capability

The procedure must be deployable for…

…extensive and/or massive Heavy Duty tractor/trailer combinations

…varying wind/temperature conditions

…public road operation in the presence of same-way and opposing
traffic 

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…

…J2263 is the accepted credible methodology for determining road force

…the voluminous data being obtained may be filtered/omitted for any
concern of validity (e.g. environmental or instrumentation anomalies)

…the positioning of instrumentation is not critical within reasonable
limits

…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.  

…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.

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.

 

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. 

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)

 



	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)

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 Va2  =  (Vr2 + 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 Vai2  -  (Vri2 + 2 w cos()*Vri + w2)]2	

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

 2 [2 Vai2  -  (Vri2 + 2 w cos()*Vri + w2)]1 * Vai2  = 0

	

 2 [2 Vai2  -  (Vri2 + 2 w cos()*Vri + w2)]1 * Vri  = 0

 2 [2 Vai2  -  (Vri2 + 2 w cos()*Vri + w2)]1 * 1 = 0

In matrix form this appears as…

 Vr2

 Vr	3

  Va2 Vr2

…and reduces to:

1		0		0		2  		=	X1	

0		1		0		-2 w cos()	=	        X2

0		0		1		-w2		= 	         X3

where X1,2,3 are the values for the unknowns as determined by the matrix
reduction.

From solution of the wind factors above, the yaw offset portion can be
solved by Cal eq 2 and Cal eq3 i.e.

  w sin() /[Vri + w cos()]

  [1 + tan(t )i tan(m )i ]

Application of the calibration factors…

The values of  and 0 are then used to correct ALL measured air
speed and measured yaw angle data for subsequent use in the J2263
analysis.

True air speed = Measured air speed measured *  

True yaw angle = Measured yaw angle + 0	

Appendix D contains numerical solutions of the form above 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 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” 

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.  

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.

the force model determines two coefficients:  Force = Am + Ca Vair2   

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

Force = Am + Bm Vroad + Ca Vair2   

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

Force = Am + Bm Vroad + Cm Vroad 2 + Ca Vair2   

Method “pj1” 

uses the calibration method as described in Analysis d)  

the force model used is

Force = Am  + Ca Vair2  (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 Vair2  (1 + P yaw2) cos (yaw) 

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

Force = Am  +  Bm Vroad   + Cm Vroad 2 + Ca Vair2  (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 Vair2   cos (yaw) 

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

Force = Am  +  Bm Vroad   + Cm Vroad 2 + Ca Vair2  

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:

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.

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.

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. 

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.

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.

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.)    

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.  

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. 

Relatively high head/tail winds are desirable for test sessions, unless
a better comprehensive calibration model is developed.  

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.

Preview all raw data and remove suspect data points affected by possible
traffic or instrumentation hick-ups.

Filter the data to at least 1 Hz or less.

Discard adjacent pairs of runs, if anomalies are found over significant
speed ranges in one or both directions.

Find the regression coefficients for the model Force = Am + Ca Vair2  . 
The yaw model is not required during principally head/tail wind
conditions.

Find the confidence intervals for all data points, by which 3-sigma data
outliers may be identified and removed. 

Determine the new regression coefficients and correct the coefficients
to mechanical and air density standards as prescribed in J2263.

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.   

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

Expanded

a + c Vi2 + 2cwVi + cw2 - Fi = 0

 i for n data points.

 - (a + c Vi2 + 2cwVi + cw2) ] 2

The unknowns can take the form of “c” which correlates with Vi2 ,
“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.

 FiVi2 – c Vi4 -2cwVi3 -(a+ cw2) Vi2 = 0

 FiVi – c Vi3 -2cwVi2 -(a+ cw2) Vi = 0

 Fi – c Vi2 -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) ] 

 Fi

 FiVi

 FiVi2

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…

  (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.

 [ (A + C V2 ) – (a + bV + c V2) ]2 dV

Taking the partials of the error squared with respect to A (=1) and C
(=V2) and then integrating gives two equations.  Notice that initial
velocity Vi and final velocity Vf influences the answer (and that makes
sense).  This convention of notation is  Vj = (Vij – Vfj) / 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

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	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.

APPENDIX D

The method described in Analysis produced the following results for the
anemometer calibration factors for different subsets of data acquired
from a pair of coastdowns as well as the resulting force coefficients
when the various cals are applied.

An abbreviated form of the J2263 coastdown force equation was used for
simplicity:

		Force = A + B V + Cm V2 + Ca Va2 (1 + P yaw2) 

Note:  Reference to “Both” indicates data was combined bor both
directions.

Cal strategy>	Used all 4 & 5 data for cal	Ignore<20mph











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





	-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



APPENDIX E

A comparison of the results for a Class 8 vehicle using various
calibration methods, force models and selections of data follows:

#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

	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	----------	----------	-3.3E-07
-1.4E-06	-1.4E-06

Ca	0.16352	0.30472	0.16352	0.12456	0.1697	0.12452	0.14568	0.14561

P	------------	----------	----------	78.6957	50.0059	78.731	-----------
----------

R-sqrd	0.4048	0.41868	0.4048	0.43093	0.432	0.43092	0.40479	0.4048

Speed	pg-1	pg-2	pg-3	pj-1	pj-2	pj-3	pj-4	pj-5

20	332.011	354.781	332.011	299.022	308.144	299.014	325.13	324.847

25	368.803	371.752	368.803	327.048	328.992	327.047	357.915	357.61

30	413.772	403.96	413.772	361.302	358.325	361.306	397.984	397.653

35	466.917	451.404	466.917	401.785	396.143	401.791	445.337	444.977

40	528.238	514.084	528.238	448.495	442.447	448.502	499.975	499.582

45	597.735	591.999	597.735	501.434	497.236	501.439	561.897	561.467

50	675.408	685.151	675.408	560.601	560.51	560.602	631.102	630.633

55	761.257	793.54	761.257	625.995	632.269	625.991	707.593	707.08

60	855.282	917.164	855.283	697.618	712.514	697.606	791.367	790.807

J1263 Am	266.602	247.441	266.602	249.197	245.151	249.202	266.855	266.602

J1263 Ca	0.16352	0.17781	0.16352	0.12456	0.12706	0.12456	0.1457	0.14561

	Confidence Intervals given Road Speed alpha at 90%



	pg-1	pg-2	pg-3	pj-1	pj-2	pj-3	pj-4	pj-5

20	20.1067	19.8707	20.1067	19.6603	19.6418	19.6604	20.1068	20.1067

25	14.2471	14.0799	14.2471	13.9308	13.9177	13.9309	14.2472	14.2471

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



#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	-4.8E-05	----------	-2.11032	0.0026	0.00111
-4.8E-05

Cm	------------	----------	-1.4E-06	----------	----------	-1.5E-07
-1.4E-06	-1.4E-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



#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	-5.5E-05	----------	-8.59097	0.0007	0.00073
-5.5E-05

Cm	------------	----------	-1.3E-06	----------	----------	-1.3E-06
-1.3E-06	-1.3E-06

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



#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	-5.5E-05	----------	-8.52458	0.0008	0.00039
-5.5E-05

Cm	------------	----------	-1.3E-06	----------	----------	-1.3E-06
-1.3E-06	-1.3E-06

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



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 PAGE   

 PAGE   2 

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

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 

Analysis c)…         Effects of Anemometer Placement

Road Speed

Observed Air Speed Vectors

Pressure profiles from vehicle air blockage

Observed Yaw Angles

Vector Relationships Against the Wind

Vector Relationships With the Wind

