# Finding the time it takes to reach 55 mph on paper

1. May 6, 2013

### dirtboi22

Finding the time it takes to reach 55 mph on paper.
You have the horse power, torque, transmission gear ratios of 1-5, rpm range, drive ratio, and primary drive ratio, and weight. You know Velocity=[(RPM*tire radius*2pi)/(Drive ratio*Gear ratio*Primary drive ratio*60)] which is velocity in ft/s . What more must you do in order to find the time it takes to reach 55 mph/80 ft/s? Is there something else I can solve for to graph against velocity in order to find this time? This is a home project of mine.

2. May 6, 2013

### dirtboi22

I am looking for a way that involves graphing, such that the area under the curve is equal to time.
I also forgot to say thank you to the ones that are taking there time to help me here!

3. May 8, 2013

### Danger

I'm afraid that I know nothing of math or graphing, including what "under the curve" means. I do, however, know a bit about cars.
A few things that you have to take into account (and I might not be using proper terminology) are your friction coefficient of the drive tires, rolling resistance (including bearing friction and brake pad drag) of those plus the "idle" tires, aerodynamic resistance, shifting efficiency (gaps decrease your acceleration)...
There are more, but those are all that come to mind right now. Ranger can probably give you a lot more.

4. May 12, 2013

### motivehunter

Assuming there is perfect traction, I can think of a way.

Start off with the equation Torque = Moment of Inertia * Angular acceleration..........E1

For each gear ratio, within the rpm of gear change, for each speed, calculate the torque based on the corresponding power value using Torque = Power/Angular Velocity and introduce appropriate reduction. Calculate the angular acceleration using E1.

Plot the angular acceleration values on the graph against time. Calculate the area under the curve keeping time t as an unknown variable to obtain the average velocity (integration of acceleration with respect to time yields velocity). Equate this angular velocity to the angular velocity corresponding to 55mph. Calculate the time.

It sure seems complex, but you're trying to model a complex scenario.

5. May 13, 2013

### Office_Shredder

Staff Emeritus
Danger listed most of the additional effects to keep in mind but a big one that is missing is the inertia of your rotating pieces. Everything that moves in the drivetrain has to be accelerated up to speed along with the linear motion of the car (for example the tires need to be spun up to speed) so the mass of the car is not the appropriate number to use for finding the acceleration of the car as a function of force.

I don't know what that number will look like for a regular vehicle but as part of an engineering project for an electric powered car that increased the effective mass of the vehicle by about 25%. The effect is going to depend on what gear you're in probably

6. May 13, 2013

### Danger

Drat! That one must have been hiding behind a tree while I was out hunting.

7. May 13, 2013

### Ranger Mike

speed calc

Danger , as always...has great insight..
here is some food for thought from the old Mopar Chassis book
One thing you have to get your arms around it the aero drag once the car is moving..it is huge and is probably the most misunderstood factor in the whole project.

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8. May 13, 2013

### mender

If you're using engine dyno graphs and not chassis dyno graphs you also have to factor in powertrain efficiency loss. A 20% drop is typical and will get you close to real numbers. This is what you actually have available at the rear wheels to accelerate the car.

After applying the 20% factor, use the torque curve to plot acceleration rates every 500 rpm for the gear ratio numbers and vehicle weight. If you just want a quick indication, take the average acceleration in each gear and figure out how much time it'll take to get through each gear. Add up the amount needed to reach 80 ft/s and you're good. For 55 mph you don't need to worry very much about aero drag unless you're quite underpowered.

9. May 13, 2013

### mender

Just a note on the first of your thumbnails: for street tires, the free diameter is the number to use. They don't grow like the slicks used in the higher classes.

10. May 14, 2013

### Danger

I just thought of something (I don't like that; it hurts my head).
Is the time stolen by spring-wrap mostly recovered when they unwind, or is it gone for good?

11. May 14, 2013

### Ranger Mike

Danger...time is a fleeting thing..as we oldsters know only too well..but

spring wrap is not desired as it detracts from a proper launch sequence. Torsional energy generated by Axel/ tire / pavement reaction is converted to heat energy when the springs wrap and shocks ( dampers) compress. Too much wrap means too soft a spring, too stiff a spring means little or no weight transfer which kills the launch. As in life there is a balance so the crew must tune the suspension to the track conditions. Time is not lost..just not beign used as effcetively as needed..

12. May 14, 2013

### Danger

Thanks, Mike.
I was unaware of that. The only track tuning that I knew of was adjusting the snubber height on the slappers. (This should go into the "jargon" puzzle thread. )

13. May 19, 2013

### jack action

You can find a calculator for that here. The complete theory is explained at the bottom of the page under Theory»»Longitudinal acceleration»»Accelerating»»Speed, distance & time.

14. May 19, 2013

### OmCheeto

Ok then. I know my next question.

---------------------------
ps. The solution to the OP's question, was the very first computer program I wrote. That would have been sometime around 1975. The equation was from either Road & Track or Car & Driver. I wrote it down, in case anyone is interested.

15. Jun 1, 2013

### Kozy

I have done similar.

I modelled a torque curve as a parabolic curve. For .1 second increments, I first determined which gear the car would be in from the previous iterations wheel speed, worked out the engine RPM from wheel speed and gear ratio, plumbed that into the parabolic engine torque equation then multiplied that figure back through the gears to give the instantaneous drive thrust at that instant. The drive thrust divided by the vehicle weight would give me an acceleration rate, and over .1 second I could then determine the additional speed and distance gained.

Rinse, repeat, then lookup 55mph for the time and distance.

16. Jun 7, 2013

### Danger

Jeez, but you had a sheltered life. I just stomped on the gas and rowed the shifter.
(And I bet that I had a lot more fun than you did.)

17. Jun 7, 2013

### Kozy

Erm, this is an engineering forum, is it not? Isn't that the sort of thing we do here?

18. Jun 7, 2013

### OmCheeto

Hey! I was 14 when I developed that software. :grumpy:
Not after we turn 16*. Then we turn to field testing our theories. Woo Hoo!

*The age at which we are not required to have an adult in the vehicle.