# Car Acceleration

by VMail
Tags: acceleration
 P: 11 Hi Im making a racing game for the XBox, I need some info on the following Gears, Gear Ratio and Acceleration, basically I want to know how a real car moves, if you are insteasted in testing the PC version then let me know Car Spec air density = 1.29kgm-3 mass = 1550kg red line = 8500rpm drag coefficient (cd) = 0.34 (not an official number) height = 1.36m width = 1.785m frontal area = height × width = 2.4276m2 (only an approximation) wheelbase = 2.665m tire = 245/40ZR18 tire radius = 0.3266m (this number is calculated from the tire spec) torque = 392Nm@4400rpm power = 206000W@6800rpm 1st gear ratio = 3.827 2nd gear ratio = 2.36 3rd gear ratio = 1.685 4th gear ratio = 1.312 5th gear ratio = 1 6th gear ratio = 0.793 reverse gear ratio = 3.28 final drive ratio = 3.545 lateral acceleration = 0.94g on skidpad of 300ft radius weight distribution (front/rear) = 57%/43 minimum turning radius = 5.6m To make things simple, the throttle can only be up or down I want to know quickly the car will move, say like from 0MPH to 30MPH, staying in 1st gear (or KPH which ever is easy, I can always convert it later) (also i havent given the distance) also Ive been given torque = 392Nm@4400rpm, how would i find the torque at 5000rpm?
P: 29
 Originally posted by VMail also Ive been given torque = 392Nm@4400rpm, how would i find the torque at 5000rpm?
Horsepower = Torque x RPM / 716

Torque in kilograms per meter --- 1kgm = 9.8 NM
Horsepower in spanish CV unit (I think its more or less same as HP) --- 1KW = 1.36 CV/HP

So you could calculate torque at 5000 rpm if you had the horsepower figure at the same egine speed.

That engine has an output of 245.81 hp at 4400 rpm and 280.16 hp at 6800 rpm.
P: 905
 Originally posted by VMail I want to know quickly the car will move, say like from 0MPH to 30MPH, staying in 1st gear
You have not specified whether it is FWD, RWD, or AWD. Especially in the first 2 cases, it will be traction-limited and the tires will have a bigger effect on acceleration 0-30 than the torque. If it is not AWD with traction control, you will also need the height of the centre of gravity, so you can calculate the weight transfer.
 Originally posted by VMail also Ive been given torque = 392Nm@4400rpm, how would i find the torque at 5000rpm?
Most modern NA engines have flat torque curves up to about 80% of redline where it begins to drop.

 P: 11 Car Acceleration most cars a FWD, so it a FWD now, and no traction I think (a lot of wheels spinning)
P: 28
 Originally posted by krab You have not specified whether it is FWD, RWD, or AWD. Especially in the first 2 cases, it will be traction-limited and the tires will have a bigger effect on acceleration 0-30 than the torque.
I don't think so. Too much traction without enough torque could hurt the launch more than a little spin off the line (been there, done that). Of course, it's easy to overpower the tires on a high-torque rwd car with regular street radials, but good drivers know how to feather the launch so that the amount of power put to the ground is balanced with the available traction. Stickier tires will allow you to launch harder and put a little less emphasis on the driver, but you'll need the low end torque or short gearing to take advantage of it.
 Sci Advisor P: 905 Low speeds like 0 to 30mph are easy because air drag is negligible. Acceleration in g's is $${f_f\over {1\over\mu} + {h\over L}}$$ where $$\inline{\mu}$$ is the lateral g's (coefficient of friction), $$\inline{f_f}$$ is the fraction of weight on the front, h is the height of the CG (I estimate 0.5m), L is the wheelbase. Plugging in your numbers gives 0.45 g's or 14.4 ft/s/s. 30mph is 44 ft/s, so the time to get there is 3.05 seconds. The same specs for RWD give 2.76 s.
 Sci Advisor P: 674 This problem is a little involved for an online forum. People take courses on this stuff. Go to the library and pick up some books on auto engineering. Even that won't help you very much with tires, since real data on them is almost impossible to come by (krab's approximation isn't very good). You'll have to experiment, and see what feels right. You'll also need a torque curve (which you can guess at from peak torque and power figures - just draw a reasonable looking graph which satisfies both conditions) at the wheels - not the usual net rating. Then you have to worry about how the differential(s) distributes torque, and the rotational inertia of the various driveline portions. Springs and shocks also affect how the car launches. If you're just making a simple arcade game (ie not a sim), then you can get away with less, but you didn't say. Ask more specific questions.
P: 11
 Originally posted by Stingray This problem is a little involved for an online forum. People take courses on this stuff. Go to the library and pick up some books on auto engineering. Even that won't help you very much with tires, since real data on them is almost impossible to come by (krab's approximation isn't very good). You'll have to experiment, and see what feels right. You'll also need a torque curve (which you can guess at from peak torque and power figures - just draw a reasonable looking graph which satisfies both conditions) at the wheels - not the usual net rating. Then you have to worry about how the differential(s) distributes torque, and the rotational inertia of the various driveline portions. Springs and shocks also affect how the car launches. If you're just making a simple arcade game (ie not a sim), then you can get away with less, but you didn't say. Ask more specific questions.
I failed A Level Physics, not because I was fick, just that I needed more time in the exam(they didnt cover any of this in the subject), yeah will be in the library in two weeks, Im learning loads of stuff on here, I though making a 3D racing car games would be easy, The game will be like Need For speed Underground, so that calculation dont have to be 100% accurate but will need to make it look realistic (also will be ignoring wind)
 P: 1,528 I'd be interested in testing the game - phatmonky@yahoo.com
 Sci Advisor P: 674 You should probably browse around this site a bit http://www.racer.nl/ He's making a game that's supposed to do the physics "right," and has a lot of documentation on it (free source too I think). It might give you some ideas.
 P: 11 I dont think krab formular is correct as there is nothing referanceing the gears
P: 905
 I dont think krab formular is correct as there is nothing referanceing the gears
Show me some data that disagrees. I've found it works very well. If you have enough power to break traction up to 30mph (which you do), then the gear ratio is not relevant; only the coefficient of friction and the downward force on the driving tires matter.

Anyway, I did the other calc.s for you.

1/4 mile: 14.11 sec @110.9 mph
top speed: 163 mph
0-60: 6.86 sec
60 ft time: 2.89 sec

A graph of driving force versus speed in each gear is here. The Green curve is your traction limit. Since the drive is FWD, this is rather low. The Red curve is air resistance. Where it crosses your white curves is top speed. The Blue curve is the performance you would get if you had an ideal gearbox which always kept you at peak power.
 P: 11 Its a bit hard for me to explain this, 1st and 2nd gear gives different acceleration eg 0-30MPH in 1st gear will take 3.05sec but what if you drive 0-15 in 1st gear and switch to 2nd from 15-30MPH both will take different times to get to 30MPH
 Sci Advisor P: 674 Well 30 mph is only 5300 rpm is 1st gear, so there would be no point in shifting before then. Shifting near 7000 rpm would be optimal for the 1->2 shift if that doesn't hit the rev limiter. If your torque curve is reasonably flat, you should be able to smoke your tires through almost all of 1st gear, so max acceleration is reached at the traction limit (part throttle). This is approximated through krab's formula.
P: 905
 Originally posted by VMail but what if you drive 0-15 in 1st gear and switch to 2nd from 15-30MPH both will take different times to get to 30MPH
15mph in second gear is only 1600rpm. You won't have enough power there, especially if it is a turbo (which I don't know). I put more realistic torque numbers in the graph. (Also the link was broken.) Look at the graph and I think you'll understand. GRAPH
 P: 11 does the graph show that top speed in 1st is approx 40MPH how would I determin how quickly the lbs goes up?