How accurate is this formula for "coast down" aerodynamic drag testing 1

Several builders of 427 cobras are headed to Boneville next year in an attempt to cross teh 200mph barrier. The current record in such a car is 198mph. We are debating the Cd of these cars and stumbled onto the following site that has some excellent information on coast down testing

http://www.teknett.com/pwp/drmayf/cdmodel.htm

Today, one of the guys did several coast down tests in his car and we had the following numbers to work with

Wt = weight
ToF = temperature
Vf = final velocity
Vi = initial velocity
P = Barometric Pressure
Af = Frontage of Car
ET = elapsed time

Wt = 3440
ToF = 75
Vf = 70
Vi = 80
P = 29.96
Af = 14.6
ET = 8.05

Cd= - 0.51135 * 3440 * 534 * ( 0.014 - 0.0125) / (29.96 * 14.6 * 8.05)

Cd = .4763

we were all excited by the results until a flight test engineer poo-poo's us and stated "the formula on teknett does not take into account mechanical friction in the F sub D (sum of all resistive forces). The formula assumes that the only resistive force is drag and ignores friction in the drivetrain, which can be significant."

My question is
Is mechanical friction REALLY that significant in our situation? We are not designing missiles that go Mach4, we are racing an old car 200mph. If we are within 10%, we would be darn happy.

Any thoughts on the issue would be appreciated.

thanks!

Andy

 

[butelja]

The faster you go, the more accurate your formula will likely be. This is because the drag power is proportional to V^3, and the drivetrain force (I think) would be proportional to lower powers of V.

 

Apart from mechanical losses in the drive train, rolling resistance plays another roll, that is the energy dissipated in deforming the tyres as they rotate. Proportionally, these mechanical forces take a greater roll when speeds come down around the 80kph mark and lower.

 

[Miper]

The test is done by measuring the speed drop over a time interval, which gives average deceleration over the interval, and therefore average force is determined. This force includes both aerodynamic forces and mechanical friction forces.

Tire and bearing friction may be significant at very low speeds, but they are probably less significant at higher speeds. There is probably data available on tire and bearing friction vs speed that will indicate how they vary and how large they are.

If you start at a high speed and take data every 10 mph during coast down, the mechanical friction part will be negligible at first and dominant at the end. Measure all the way down to , say, 5 - 15 mph. The calculated resistance in this speed range could be assigned entirely to mechanical friction. Subtract this figure from the higher speed cases. Now you have a good approximation to the actual aerodynamic drag.

Aero forces are proportional to velocity squared (not cubed as butelja states -- power is proportional to speed cubed, aero forces are proportional to speed squared). So at 200 mph and a drag coeff. of .4, the drag force on a small car might be about 400 lb. At 100 mph, this is 100 lb, at 50 mph this is 25 lb, at 25 mph it is a little over 6 lb, and at 10 mph it is barely 1 lb.

It is important to know temperatures and air pressure so you can get the proper value for air density. It is also best to run at high tire pressures and to test in zero wind conditions. Large temperature variations will also affect the rolling resistance.

It is difficult to get exact drag numbers reduced to equivalent standard temperature and pressure conditions from one day to the next. Nevertheless, you can run A - B tests on different configurations in equivalent atmospheric conditions and still know which is lower drag, even if the actual drag numbers are elusive.

 

[vtl]

How come Ft = 0
isn't that Ft = ma

 

[Miper]

to vtl:
Since there is no Ft in the above discussion, I assume you are referring to the Ft in the linked article referenced above. That article says:
___________________________
"Ft = 0

why?
well, Ft = 0 because we have slipped the tranny into nuetral and we are coasting!"
_____________________________

qed

 

[mrvortex]

I've done hundreds of miles of coast down testing in an attempt to avoid $2,000+ per hour WT costs at Lockheed-Georgia. and find it extrememly frustrating. The scatter in the data is surprisingly large, which creates errors that render small drag changes difficult to find. By the way, at freeway speeds rolling drag is surprisingly close to 1/3 of total drag - whether you're talking about a Porsche or an 18-wheeler! It is a good simplifying assumption to make when analyzing your drag data.

I've discovered a much better way to check aero drag of a street vehicle is to coast down a long straight hill on an Interstate highway with a fixed gradient. Get the vehicle up to equilibrium speed near the top of the hill and coast in neutral. If you take pains to get the diff., wheel brgs, and tires etc. up to operating temp before you start a series of test runs, you will be surprised how repeatable and sensitive your speedometer readings will be. This method is so sensitive that you'll find you'll have to add ballast to correct for the fuel burn during a few test runs! You can easily pick up differences in total drag as small as 1 or 2% and that's terribly hard to find in coast-down tests. Just remember that Cd changes at the square of any velocity changes you detect. - - mrvortex.

 

[poetix99]

Just a proofreading comment: I think that mrvortex meant "...remember that DRAG FORCE changes as the ratio of the velocities squared"

It is, of course, not Cd that changes.

 

[mrvortex]

Grin, that's what I get for tech talk when weary.... mrvortex

 

[poetix99]

Better asleep at the monitor of your computer than at the steering wheel of your car; even if only doing coast-down tests.

 

[mrvortex]

A note from an old Indy Car designer: My good friend Miper, being an aircraft guy more than a car guy, is wrong about the rolling drag component of a car's total drag being of nearly fixed magnitude in his May 22 post. Goodyear Racing Division data shows that rolling drag changes approx. linear with changes in vehicle speed. Similarly, for purposes of coast-down or hill-coast drag measurements, it is a good simplifying assumption that wheel bearing and differential gear friction and pumping losses also change linearly with vehicle speed. Bottom line is that rolling drag force at 60 mph is roughly six times the magnitude at 10 mph. And since rolling drag turns out to be surprisingly close to 1/3 of total vehicle drag for most automobiles at freeway speeds, that too is a helpful simplifying assumption for coasting tests conducted on a steep Interstate hill. -- mrvortex

 

[Miper]

I knew I was over my head on some of the automotive details. That's why I asked my friend, mrvortex, to enter the thread. He is the expert on this subject. His understanding of coast-down drag testing is second to none, and he has provided excellent information here on how to conduct and interpret the results of a coast-down test.

miper

 

[mechclanky]

Hi,

I know this thread is a little old but I was hoping that I could get your thoughts on this issue with a little twist.

I am carrying out a series of tests on motorised kick scooters, both electric and 2-stroke.

What problems would i have when trying to carry out a coastdown test on a vehicle with a top speed of 20kmh and do you have any potential solutions? How much effet would the rider have on the Cd of the scooter?

Cheers

Ed

 

[GregLocock]

Last question first:enormous

Your main problem will be that Crr dominates at such low speeds, so you will find it difficult to measure CdA (the power vs speed curve will be mostly parabolic).

Perhaps you might get a better estimate of CdA by measuring the force on a stationary scooter, pointed into the wind.

Cheers

Greg Locock

 

[mechclanky]

Now there is a thought, thanks for that!!


Cheers

Ed

 

[cdx]

Mrvortex, I found your post very informative.
You mentioned the problems with coast down testing on a flat surface, and suggested using an inclined surface instead.
The test you described seemed very simple - just get up to speed, slap the car into neutral, and coast while recording the time from speed A to speed B.
My question is : Once you have attained the time from ..say 80 mph to .. 10 mph, then what ?
What other information is needed to record the cars .cd figure and how would it be computed ?
( An example would be great ) -Thanks

 

[Tmoose]

cdx - according to his profile Mrvortex last logged on Sep 2002 ! His webpage

http://www.streamlining.com/

is http 404 also. I am saddened.

 

[LoveLearn]

I've been involved with coast down testing since when Tapley 5th wheels and mechanical clock drive paper strip chart recorders were considered state of the art rather than antique curiosities. It seems to me that the best way to isolate wind friction from all other combined linear frictions is to test friction at speeds just above bearing breakaway speeds but with all bearings and tires fully warmed. I've pushed an 18,000 GMC bus to walking speed by hand on level pavement. At those speeds a walking 2 year old baby could push a sign as big as a highway bus through the air without working hard if the sign were mounted on a soap box derby car inside a windless auditorium. Wind friction at really low speeds is really small. Linear friction stays the same and pushing that bus still takes a real effort.

So attach a steady speed pulling device to your load making sure the pull vector is level and aligned with the pulled vehicle's direction, but insert a spring scale between them in the pulling line. A garden tractor in creeper low gear will do nicely. You need to read the tension and record the speed. You can calculate speed using a stopwatch to count seconds between some ground marks a known distance apart. You only need one point on a linear curve. Then you can deduct that line from the total coast down friction curve. The balance is wind friction. I just assume that at 1/2 mph all pulling tension on windless days relates to linear friction. Not elegant but it works well enough.

As to the 1/3 of friction comment, that only occurs at one speed. Below that speed the percentage is higher, above that speed the percentage is lower. It's just an intersection point, not a rule of thumb.

Lots of nice shaft rotation sensor triggered systems are now available that allow laptop computer clock based data stream capture logging. Once you have that data stream and the other already discussed data, you have a very powerful performance testing tool. Push it through a spread sheet and derive all the values you want.
John

 

[sailoday28]

Isn't Cd a function of Reynolds Number (rho * V*Length/viscosity)?

 

[MoreWing]

One way to quanitify the mechanical part of the drag number is to do a series of low speed coast downs. I did a day of coast downs with a racecar and at the end we did a couple 30mph to 5mph coasts. This maybe wasn't perfect as the mechanical drag is no doubt a function of speed, but it did allow me to at least have some sort of mechanical drag component in my calculations. I figured at those speeds, the drag had to be primarily mechanical.

A couple years later I got wind tunnel data for the car and found that my numbers were not too bad. Directionally, they were right on, but the tunnel was much more optimistic in terms of Cl and Cd that I was. Interesting experiment anyhow.