Acceleration at given speed

[edb49]

I'm running through some numbers in Excel on my car (Caterham R500) trying to get a better understanding of performance.

For the sake of simplicity I always assume the engine is pushing out peak power, and I'm using a CdA (in sqft) of 9.17 for the car. What I've done is calculate "spare" BHP at any given speed, and then from this I've calculated the G-force in acceleration the car could produce at a speed.

To pick out some values:

60mph - 0.97g
100mph - 0.44g
130mph - 0.13g

Do they all look sensible? The thing I can't quite understand is at lower speeds I get massive readings, e.g. at 5mph the car can pull 12g, and 10mph 6g. Obviously it is grip-limited at these speeds, but if it had unlimited grip and you could access peak power at those speeds, is that what would happen?

[anonymous-user]

in simple terms, yes!

F=MA, so if you can get all of F to the ground, then (as M is constant) you get A.


But of course, what you actually get is lots of wheelspin, and to get peak power at all roadspeeds would either need a CVT, or a eleventybillion speed DCT !!! ;-) (or a controlled clutch a-la dragster)


Editted to add: You can get quite accurate EXCEL vehicle accel models quite easily, but they all fall over on accurately determining things like traction, clutch engagment, etc etc.

If you make your excel sheet "driven" by road speed, then you can easily work backwards and iteratively to get engine power (then calc the vehicle accel if you split time down into small enough segments (say 1ms) then the fact that the accel for the next segment is actually using the engine power from the last segement ceases to matter and the velocity/distance integrate fine)

Edited by anonymous-user on Thursday 16th September 11:14

Edited by anonymous-user on Thursday 16th September 11:15

[edb49]

Cool, thank you! Going to play around a little bit more, glad I'm on the right lines...

[Pumaracing]

It's not that complicated to program a proper simulation spreadsheet that takes into account gearing, drag, torque curve, tyre radius and other factors that affect vehicle performance. Most of the maths is on my website in the following articles.

http://www.pumaracing.co.uk/TOPSPEED.htm

http://www.pumaracing.co.uk/simulate.htm

http://www.pumaracing.co.uk/FLYWHEEL.htm

http://www.pumaracing.co.uk/trans.htm

The inertia calculations are the most complex part but as I indicate they can be simplified with certain assumptions although doing it properly is much better.

Your results are because when you work through all the maths it turns out that acceleration (ignoring gearing) is proportional to power / road speed.

As speed tends towards zero then acceleration tends towards infinity but of course actual gearing limits the available torque at a given speed.

A good explanation of that is given here.

http://craig.backfire.ca/pages/autos/horsepower

Without taking actual gearing into account you'll never get close to a true simulation of how a vehicle will accelerate so I suggest you go back to basics and work it out properly from torque and rpm.

[edb49]

Thanks for everyone's help, I've re-done my spreadsheet with a few different assumptions and ended up with something that looks relatively sensible:

http://dl.dropbox.com/u/473116/acceleration.png

(Acceleration in G at a given speed)

I've just put in a GT-R and Caterham R500 as example vehicles. It takes into account air resistance, gearing, etc. It assumes constant torque at any RPM which I think is a reasonable assumption for most modern engines in the power band you'd use them.

[Pumaracing]

edb49 said:

It assumes constant torque at any RPM which I think is a reasonable assumption for most modern engines in the power band you'd use them.

Not really. Torque is falling pretty fast as the engine approaches peak power and especially beyond that and to get the best acceleration you do need to rev any engine about 500 rpm past the point of peak power. By the time you reach a gearchange point torque will be maybe 20% less than what it rises to again at the revs the next gear kicks in at.

Also your cars are accelerating during the gearchanges which could do with fixing. However other than the above it does look closer to reality.

[edb49]

Pumaracing said:

edb49 said:

It assumes constant torque at any RPM which I think is a reasonable assumption for most modern engines in the power band you'd use them.

Not really. Torque is falling pretty fast as the engine approaches peak power and especially beyond that and to get the best acceleration you do need to rev any engine about 500 rpm past the point of peak power. By the time you reach a gearchange point torque will be maybe 20% less than what it rises to again at the revs the next gear kicks in at.

Also your cars are accelerating during the gearchanges which could do with fixing. However other than the above it does look closer to reality.

Yep, I know the torque model isn't prefect but I'm only after something fairly rough. The reason for the acceleration during gear changes is because I'm modelling at 5mph increments, fairly easy to fix.

The model calculates a Boxster S as 0-60 in 5.2s, GT-R as 3.1s, Caterham R500 as 2.8s. These are all pretty close to manufacturer's quoted times... which I'm pretty pleased with

[Slinky]

Looks like you're doing some good stuff there chap, any chance of sharing your sheet?

[edb49]

Slinky said:

Looks like you're doing some good stuff there chap, any chance of sharing your sheet?

It wouldn't be very helpful, because there is some stuff I do manually:

1) Gear ratios, adjusting every acceleration figure for them
2) "Time lost" in 0-60s for shifting

It's one of those things that wouldn't be much help to anyone, but you're welcome to it if you're bored on a Fri afternoon at work

[Pumaracing]

edb49 said:

Yep, I know the torque model isn't prefect but I'm only after something fairly rough. The reason for the acceleration during gear changes is because I'm modelling at 5mph increments, fairly easy to fix.

The model calculates a Boxster S as 0-60 in 5.2s, GT-R as 3.1s, Caterham R500 as 2.8s. These are all pretty close to manufacturer's quoted times... which I'm pretty pleased with

The trouble with 0-60 times on fast cars like those is they are mainly grip limited so you can "fix" the desired time as you tinker with the grip limit factor and gearing. Any surplus power just goes to waste. If you also "fix" the drag factor to obtain the desired top speed then the whole curve can be close to reality without the program actually doing anything properly.

My own program (also a spreadsheet) has evolved over nearly 20 years but now takes into account the following.

Actual gearing
Actual torque curve
Transmission and tyre bhp losses
Clutch engagement rpm
Peak engine rpm either limited or the program will select the optimum from the torque curve and gearing.
Gear change time
Actual frontal area and Cd
Tyre rolling resistance
Tyre grip under acceleration
Tyre grip under braking (usually higher especially with 2wd vehicles)
Inertia of engine speed items - crank and flywheel masses
Inertia of wheel speed items - wheel and tyre masses
Headwinds
Tailwinds
Gradients either up or down
Downforce for F1 and other high downforce type vehicles which rely on it for grip. Both acceleration grip and braking grip are modified separately by the downforce.
Braking time and distance calculations using mechanical tyre grip, downforce aided tyre grip as well as aero drag which can include Veyron type air dams.
Speed increment variable of 1 mph for 200 program lines up to 200 mph but I can change the variable to anything else I want to allow for higher top speeds or finer detail of smaller speed increments.

It then prints out a full Autocar type test sheet with in gear-times every 20 mph, 0 to top speed times and distances in 10 mph increments, 60ft, 220 yard and 1/4 mile times and speeds for drag racing, optimum gear change points for each gear to maximise acceleration.

It's been somewhat of a labour of love over the years but it's very helpful in analysing car performance for my business.

Edited by Pumaracing on Saturday 18th September 09:59