Roll-down test to determine rolling and aero coefficients

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Roll-down test to determine rolling and aero coefficients

jeremy.rutman-2
Hi All
I finally got around to working out the math for the roll-down test.  
This is where you find the aero and rolling drag coefficients from rolldown
times on a flat straight road with no traffic.  
If you don’t want the math you can skip to the part where the step-by-step is
laid out.
The acceleration from rolling and aero drag is reputedly
Acceleration = -Crr g – (rho Cd A / 2m) v^2
To clean it up I call the first term a and the second b:
Acceleration = -a - b v^2
This diff equation is solved to give
v_start = sqrt(a/b) Atan(sqrt(ab) t)
where v_start is your starting speed and t is the time taken for roll-down.

We’d like to do two tests and then have two points on a curve from which a and b
could be found.  
But the equation cant be solved cleanly, (anyone who wants to give it a crack
pls let me know if you get somewhere)
so we can break this into two parts, a slow test for finding ‘a’ and a fast one
where both a and b are in play.
From the range of expected values of a and b (a between 0.06m/s^2 to 0.2m/s^2,
and b between  0.0024/m and 0.00012/m)  
I find that the linear parts of the Atan curves are below about 10-15km/hr for
cars and trucks (bikes maybe later).  
So a possible procedure is:

Step 1 – find a
Do a few tests at different low speeds (below 10-15km/hr).
Drive at a steady low speed, and start timing the moment you take your foot off
the electrons.
Stop timing as soon as you come to a stop.  
v_start is your starting speed and t is the time it took to roll to a stop.
Take the ratio v_start / t ; this is your  value of a
(remember a is my abbreviation for Crr g)
These values should come out the same each time you do the low-speed test, if
you are starting slow enough.
If you don’t trust your speedometer you can do this more accurately by measuring
roll-down distance d and time t, with
Crr g = 2d/t^2 (still at low speeds).

Step 2 – find b
Now do a test with high starting speed (where wind resistance is important, e.g.
70km/hr or more).
We have to solve v_start = sqrt(a/b) Atan(sqrt(ab) t) for the unknown b, which
one can do with a calculator and iteration (or excel/mathematica/matlab),
or by using some graphs I put up at
http://physics.technion.ac.il/~rutman/car/Roll-down%20test.pdf
or by using the following tables constructed for the case of starting
velocity=70km/hr (44 mph).  
If you want to use the tables you have to start from 44mph.
Use the table with the closest value of a (which you found in the first step).

a= 0.06
 Time= 270.   b=0.00011
 Time= 254.   b=0.00016
 Time= 238.   b=0.00022
 Time= 222.   b=0.00030
 Time= 206.   b=0.00040
 Time= 190.   b=0.00053
 Time= 174.   b=0.00070
 Time= 158.   b=0.00093
 Time= 142.   b=0.00124
 Time= 126.   b=0.00170
 Time= 110.   b=0.00239

a= 0.08
 Time= 200.    b=0.00016
 Time= 189.5   b=0.00022
 Time= 179.    b=0.00029
 Time= 168.5   b=0.00038
 Time= 158.    b=0.00049
 Time= 147.5   b=0.00062
 Time= 137.    b=0.00080
 Time= 126.5   b=0.00102
 Time= 116.    b=0.00131
 Time= 105.5   b=0.00170
 Time= 95.     b=0.00224

a= 0.1
 Time= 170.   b=0.00013
 Time= 161.   b=0.00019
 Time= 152.   b=0.00027
 Time= 143.   b=0.00037
 Time= 134.   b=0.00049
 Time= 125.   b=0.00064
 Time= 116.   b=0.00083
 Time= 107.   b=0.00108
 Time= 98.   b=0.00140
 Time= 89.   b=0.00184
 Time= 80.   b=0.00245

a= 0.13
 Time= 130.   b=0.00017
 Time= 124.   b=0.00025
 Time= 118.   b=0.00033
 Time= 112.   b=0.00044
 Time= 106.   b=0.00056
 Time= 100.   b=0.00071
 Time= 94.   b=0.00090
 Time= 88.   b=0.00113
 Time= 82.   b=0.00141
 Time= 76.   b=0.00178
 Time= 70.   b=0.00225

a= 0.16
 Time= 110.   b=0.00014
 Time= 105.   b=0.00022
 Time= 100.   b=0.00032
 Time= 95.   b=0.00043
 Time= 90.   b=0.00057
 Time= 85.   b=0.00073
 Time= 80.   b=0.00093
 Time= 75.   b=0.00118
 Time= 70.   b=0.00149
 Time= 65.   b=0.00188
 Time= 60.   b=0.00238

a= 0.18
 Time= 100.   b=0.00012
 Time= 95.5   b=0.00020
 Time= 91.    b=0.00030
 Time= 86.5   b=0.00042
 Time= 82.    b=0.00057
 Time= 77.5   b=0.00074
 Time= 73.    b=0.00095
 Time= 68.5   b=0.00120
 Time= 64.    b=0.00152
 Time= 59.5   b=0.00193
 Time= 55.   b=0.00245

a= 0.2
 Time= 90.   b=0.00013
 Time= 86.   b=0.00022
 Time= 82.   b=0.00033
 Time= 78.   b=0.00046
 Time= 74.   b=0.00062
 Time= 70.   b=0.00081
 Time= 66.   b=0.00103
 Time= 62.   b=0.00131
 Time= 58.   b=0.00166
 Time= 54.   b=0.00209
 Time= 50.   b=0.00264

You now have your drag and aero coefficients a and b, where
a=Crr g  and b=rho Cd A / 2m.    rho is the density of air, 1.2kg/m^3 at sea
level, A is vehicle projected frontal area,
m mass, g gravitational acceleration, 9.8m/s^2 at sea level.
The precision of a and b here will be something like the precision of your
measurements but I haven’t worked out the relation, maybe later.
Anyone with the heart to check the maths please do so, there may be mistakes in
here.
Anyone who actually does the tests let me know how they worked out, what your
values of a and b were.  
More info at http://physics.technion.ac.il/~rutman/car/Roll-down%20test.pdf
-jeremy rutman






Jeremy Rutman
Technion Physics Dep't.
Haifa 32000 Israel
phone 972 4 8293669
fax   972 4 8295755

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Re: Roll-down test to determine rolling and aero coefficients

Jeff Shanab
Thanks. My rig is so inefficient I really need to look closely at this
and give it a try. The first question I have is if the relation ship is
linear enough to use rolling to a stop as a point. Maybe slowing to
5,10,15,20 mph would give a better indication of the rolling
resistance?. It seems when I push a car that it takes more force to get
it rolling that to keep it rolling. like static and dynamic coefficients
of friction.

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Re: co-efficent of drag

FRED JEANETTE MERTENS
how do you figure co-efficient of drag after I put fender skirts' front and rear ; smooth skinned the bottom for aerodynamics ' and found a way to reduce the drag from the vacuum in the rear between the tail lights ?
  ----- Original Message -----
  From: Jeff Shanab<mailto:[hidden email]>
  To: [hidden email]<mailto:[hidden email]>
  Sent: Sunday, August 12, 2007 3:29 PM
  Subject: Re: [EVDL] Roll-down test to determine rolling and aero coefficients


  Thanks. My rig is so inefficient I really need to look closely at this
  and give it a try. The first question I have is if the relation ship is
  linear enough to use rolling to a stop as a point. Maybe slowing to
  5,10,15,20 mph would give a better indication of the rolling
  resistance?. It seems when I push a car that it takes more force to get
  it rolling that to keep it rolling. like static and dynamic coefficients
  of friction.

  _______________________________________________
  For subscription options, see
  http://lists.sjsu.edu/mailman/listinfo/ev<http://lists.sjsu.edu/mailman/listinfo/ev>
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Re: co-efficent of drag

Lee Hart
From: FRED JEANETTE MERTENS
> How do you figure co-efficient of drag after I put fender skirts
> front and rear; smooth skinned the bottom for aerodynamics and
> found a way to reduce the drag from the vacuum in the rear between
> the tail lights?

You can use the technique outlined in a recent previous email describing the roll-down method. However, what you really care about is the end result -- does your EV use less power to drive at any given speed?

So, all you need to do is drive on a particular route at a particular speed, and record the power used. Do it a number of times, in both directions, etc. (For instance, use your regular daily commute or other drive you regularly make).

Now make one change (fender skirt, belly pan, tire pressure, or whatever), and repeat the test to see what change it produced. Again, your results will be more accurate if you repeat the test several times. Often, a small change produces such a small result that you need to repeat the test many times to be sure you aren't just seeing random changes.


--
"Excellence does not require perfection." -- Henry James
--
Lee A. Hart, 814 8th Ave N, Sartell MN 56377, leeahart-at-earthlink.net

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Re: Roll-down test to determine rolling and aero coefficients

jeremy.rutman-2
In reply to this post by jeremy.rutman-2
If nonlinear rolling resistance or static vs dynamic effects are really a
problem you could do as you mention,
e.g. time the coast from 10km/h to 5km/h
and also the coast from 5km/h to 0, they should come out the same.
(If you have a timer with 'lap'
it will finally come in handy)
I havent seen many speedometers that actually measure decently on the low end
so you could try another way using distance and time instead of velocity:
Put 3 markers evenly spaced (e.g. at 0, 20meters, and 40meters).
Hit the timer as soon as you coast past the 1st marker.
Hit lap as soon as you coast past the 2nd marker
Hit stop as soon as you coast past the 3rd marker.
What you want is the time from 1st to 2nd marker and time from 1st (not 2nd) to
3rd marker.
If you manage to get those times you can use
a=Crr g = 2 (x1 t2 - x2 t1)/(t1 t2 (t2-t1))
where x1 is distance between 1st and 2nd marker
x2 is distance between 1st and 3rd marker
t1 is time from 1st to 2nd marker
t2 is time from 1st to 3rd marker
thats your value of Crr g, (rolling resistance coeff x gravity)


Death to All Spammers where are you?? You asked for this analysis about half a
year ago,I blew a Sunday on it so stop killing spammers and start measuring!

On Sun, 12 Aug 2007 13:29:40 Jeff Shanab wrote:
>Thanks. My rig is so inefficient I really need to look closely at this
>and give it a try. The first question I have is if the relation ship is
>linear enough to use rolling to a stop as a point. Maybe slowing to
>5,10,15,20 mph would give a better indication of the rolling
>resistance?. It seems when I push a car that it takes more force to get
>it rolling that to keep it rolling. like static and dynamic coefficients
>of friction.



Jeremy Rutman
Technion Physics Dep't.
Haifa 32000 Israel
phone 972 4 8293669
fax   972 4 8295755

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Re: Roll-down test to determine rolling and aero coefficients

jeremy.rutman-2
In reply to this post by jeremy.rutman-2
The test I outlined will work no matter what kind of setup you have.
If you want to see the changes due to your mods, test once before mods
and once after mods and see how the coefficients change.
again, the full test description is at
http://physics.technion.ac.il/~rutman/car/Roll-down%20test.pdf

or as was mentioned you can just run a set route a bunch of times and forget
the
quantitative stuff. On the other hand the White Zombie dude can surely tell you
theres nothing like hard numbers (e.g. quarter mile time) to cut the wheat from
the chaff, and those coeficients are directly comparable to other rigs.

On Sun, 12 Aug 2007 "FRED JEANETTE MERTENS" wrote:

>how do you figure co-efficient of drag after I put fender skirts' front and
>rear smooth skinned the bottom for aerodynamics ' and found a way to reduce
the
>drag from the vacuum in the rear between the tail lights ?

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Re: Roll-down test to determine rolling and aero coefficients

Jeff Shanab
In reply to this post by jeremy.rutman-2
What I am most interested in in this test is to isolate the majority of
my losses to aero vs rolling I drive the same route to work every day
and it is a pretty constant amount.

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