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I am trying to model a speedometer and tachometer for a simple software model of a car dashboard. I want this to be relatively simple, so for my purposes I won't likely simulate variables such as drag (or, assume that drag is a constant). But I would like to know the general formulas for:

1) Calculating the RPM, depending on a position of a graphical slider representing the accelerator.

2) Using this information to find the instantaneous speed (or, magnitude of instantaneous velocity?).

I am not sure, in the case of 2), what other independent variables I need to consider. Do I need to consider the frequency of rotation of the wheels (assuming a fixed radius), in addition to the RPM?

If anyone can give me a rough explanation plus relevant formulas, or alternatively direct me to other trusted resources online (I have had a hard time sifting through info and determining the accuracy), it would be much appreciated.

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It sounds like your simulator consists of an accelerators and the feedback of the tach and speedometer and these are connected together through the model of the accelerating car. Let's neglect tires slipping. The accelerator induces a power that generally depends on the engine speed. Let the car have about one hundred horsepower which is 7500 watts of power and you could just scale this linearly with engine speed afer reading about that online.

look here to convert the horsepower to torque and then use the torque and force relation involving the radius of the tire to get the linear force acting on the car due to to the tires. Chose a sensible mass for the car and get your acceleration. From there you just use kinematic equations to get the speed which you would display at the speedometer. You will also have to model the drive train and gear ratio it seems.

It's possible that there is just a linear relationship between the tach speed and the car speed. That's probably the gear ratio.

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I now understand the formula for calculating torque. However, I am not clear based on your description how to calculate the acceleration once I have the torque. "Choose a sensible mass for the car and get your acceleration". What does this mean precisely? Can you give an example? Thanks. –  Dylan Jun 7 '12 at 2:06
    
F = mass * acceleration perhaps? So to get the acceleration, F/mass? Is this the correct approach? –  Dylan Jun 7 '12 at 2:13
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