Cd and Frontal Area

[Rusty]

For a coupe please. I'm looking into doing some rough calcs using my free GPS program and some maths.

If I can get a 5Hz or 10Hz GPS receiver for good money then this might be an ultra cheap alternative to something like a GTech or more expensive GPS jobbie. I like number crunching and I also like saving money on stuff. Excel and a mobile are free and there are loads of GPS data loggers. Job done. Will report on my progress on a new thread. Not after massive accuracy, just whether I can get meaningful data with the proviso that it's subject to small errors. Hoping that with the Cd and area I can calculate rough bhp resistance for power calcs. Just for fun really!

[Mcstiff]

CD for a Coupe Quattro is .36 not sure for a S2 or RS2

[K Simmonds]

According to my 1990 Audi Coupe brochure the Cd is just 0.29, very impressive for the time. The figures for the US cars are most likely different due the crappy front bumpers fitted to Coupes in the states.

[Rusty]

I was thinking in the 0.3 region from delving into the old grey matter. 0.36 seems too high, that might be for a typ85 thinking back rather that the typ89. Will get a tape measure out to guess frontal area I think, seems as good a method as any.

[Rusty]

Carfolio has Cd at 0.32 and frontal area at 1.89m^2.

[Rusty]

From those numbers I've calculated that the air resistance at 100mph (44.7m/s) =

P = power (W)
F = Force (N)
v = velocity (m/s) = 44.7m/s
rho = density (kg/m^3) = 1.25 for air.
Cd = Drag coefficient = 0.32
Af = Frontal area (m^2) = 1.89

P = F.v
F = 1/2.rho.Cd.Af.v^2

Combining:-

P = (rho.Cd.Af.v^3 )/2

With the numbers above:-

P = (1.25 x 0.32 x 1.89 x 44.7^3)/2
P = (0.756 x 89315)/2 = 33.8kW

1kW = 1.341bhp so

= 45.3bhp

Of course, this is bhp at the wheels so using my transmission losses from a previous RR session:-

Approximate RPM for 100mph and flywheel power:-

3rd 7000 = 1.50 = 68 bhp
4th 6000 = 1.35 = 61 bhp
5th 5000 = 1.25 = 57 bhp
6th 4000 = 1.20 = 54 bhp

[Rusty]

I've also found some data for rolling resistance.

F = Cr.m.g

Where:-

F = Force (N)
Cr = Rolling resistance coefficient = 0.015 for road tyres
m = mass (kg) = 1525 + 25 + 100 = 1650kg for me in a car with 1.2 tank of petrol
g = gravity (m/s^2) = 9.81 m/s^2

So from above:-

F = Cr.m.g
F = 0.015 x 1650 x 9.81
F = 243N (assumed constant)

[EspenW]

Don't bother with rolling resistance. You want true ATW numbers like those from a dyno.
BTW, Cd of the RS2 is 0.35 according to the only source that I have seen (test in Autocar). I use that along with the frontal area of the RS4 (2.04 m^2).
The coupe should be somewhat sleeker, so your data seems correct

[Rusty]

Yeah, I've edited my calcs and used the losses from a previos rolling road session to guestimate flywheel hp. Interesting that on a GTech power run you'll be losing equivalent to ~ 68bhp (at the fly) due to air resistance. You would need to take this into account as that's a large number!

[stiglet]

At speeds like 100mph the tyre resistance becomes very pointless. You could get away with just looking at aero drag.

Andy, if you want a little bit of fun, work out your theoretical top speed then compare this with actual and see how close you get. You'll have to use gearing in 6th and look at a power curve to try and match the drag and power at given speed.

[anton]

good bit of calculations.....will be useful! they seem a bit low however..., i know my cq20v tops out at 145 on the speedo....135mph in real life at a guess with 180bhp, take top speed of 140mph as an extreem possibility, and 180bhp for minimum.......therefore at 140; air resistance, transmission loss and rolling resistance should all equal lets say 160bhp as it tops out at about 6500rpm, 180 hits at 7000.

my dyno came out as a rolling resistance and transmission loss of 50bhp, possibly 60 or 70 as its 5th gear not 4th (putting resistance of cv joints ect in as rolling res.).....that leaves about 110bhp aerodynamic resistance 140mph, with the formula it works out at 88.8bhp at 140...

perhaps the CD or frontal are are larger?.....if the rs2 is 3.5, then 3.6 could well be accurate for the coupe.....the rear screen is close to the critical angle, if the air is separating then the avant will probably be more aerodynamic......

unless theres something else i'm forgetting?...

Ant

[anton]

lol Stiglet got there first with the top speed test!

Ant

[stiglet]

CD changes with speed, it's not a fixed value. Doesn't change by much though. Did you remember to convert BHP to watts and speed to m/s?

[anton]

no, i just read the first equation, only v varies, so divided by 44.7^2 and multiplied by 62.6^2.......gets 88.8bhp.....

yeah you guessed it....i'm stupid...it's cubed....was thinking squared was not enough...just didnt read it correctly....done it again and got 124bhp......

So all calcs look 100% spot on to me
bare in mind the top speed and power for my car i used were limits not actual values, power is likely 10bhp more and speed about 5mhp less.....

Ant

[Rusty]

The aim is to be able to use data logging from the GPS on my phone to give theoretical power at the fly, power at the wheels and to compare performance data. Saves about £200 on a GTech and £££s on a VBox. The data doesn't have to be ultra accurate but race chrono state +- 0.15s with a 5Hz GPS device so that's not too bad.

Taking 192bhp (142kW) at the wheels at 7k RPM (from a RR graph) and the data above, the theoretical max is 174mph or 78m/s. I'd say that's a touch optimistic, more like 160mph seems realistic. Of course the losses were in 4th gear not 6th so there is still some mechanical advantage rather than disadvantage. Sticking to performance figures around the region tested (120mph max) I think the accuracy will be plenty good enough to compare modifications.

The next step is to get a 5Hz GPS jobbie and do some back to back runs and see how repeatable it all is. I've got 6GB of memory to use up and it's pretty frugal so all good.

Watch this space (well actually the new thread I'll write on it )