Physics of a turning car
Let's say a car is moving at velocity v.
The car then decides to turn with wheel angle a.
Known properties of the car that may be relevant: wheel base (from front wheel to back wheel center), forward vector, up vector.
I want to know the radius of the turn so that I may position the car correctly by finding the angle of the radius.
I have some idea of this, but I have no idea of how the wheel base plays into this. All topics only simply deal with friction, which I do understand, but for some reason I can't figure out how to do this simple math problem.
Thanks!
P.S. Don't go math crazy on me, but links to helpful resources are still great. I'm only 16.
This tutorial might be useful if you haven't seen it already.
The position of the wheel relative to the center of the car is used to convert any forces that the wheel applies to the car-body into torques - these torques are then used to rotate the car-body. The above link explains the math behind this ;)
That's not easy to find, as the radius differs depending on how fast the car was going when it started to turn (and whether it accelerated/braked while turning).
In a realistic simulation, when you turn the front wheels the friction caused by the road exerts a horizontal force (perpendicular to the forward direction of the wheels) on the car, which is converted into a torque, which then causes the car to rotate.
So really, the rate at which the car turns is determined by the friction between the wheels and the ground, which is dependent on steering angles, velocity, etc...
Furthermore, in a realistic simulation, if you're accelerating/braking while turning it will change the amount of friction acting on the wheels, which can alter the turning rate.
Quote:Original post by solinent
I have some idea of this, but I have no idea of how the wheel base plays into this. All topics only simply deal with friction, which I do understand, but for some reason I can't figure out how to do this simple math problem.
The position of the wheel relative to the center of the car is used to convert any forces that the wheel applies to the car-body into torques - these torques are then used to rotate the car-body. The above link explains the math behind this ;)
Quote:Original post by solinent
I want to know the radius of the turn so that I may position the car correctly by finding the angle of the radius.
That's not easy to find, as the radius differs depending on how fast the car was going when it started to turn (and whether it accelerated/braked while turning).
In a realistic simulation, when you turn the front wheels the friction caused by the road exerts a horizontal force (perpendicular to the forward direction of the wheels) on the car, which is converted into a torque, which then causes the car to rotate.
So really, the rate at which the car turns is determined by the friction between the wheels and the ground, which is dependent on steering angles, velocity, etc...
Furthermore, in a realistic simulation, if you're accelerating/braking while turning it will change the amount of friction acting on the wheels, which can alter the turning rate.
Let's ignore the physics of a turning car (which is horrible and complicated), and instead look at the geometry of a turning car. That's also relatively horrible when one approaches it as an exact problem, but we can simplify it a little bit. Check out this diagram:
The car is traveling in the circle shown. Note that its upper wheel is perpendicular to the "r" line segment, and so its angle (which we'll call θ and pronounce "theta") is the same angle that the r line makes with the horizontal. Note also that we know the distance "a", as the distance from the front wheel to the back wheel. A little bit of trig gets us:
r = a / sin(θ)
There's numerous simplifications here, but for sane values of a and θ they won't be noticeable.
The car is traveling in the circle shown. Note that its upper wheel is perpendicular to the "r" line segment, and so its angle (which we'll call θ and pronounce "theta") is the same angle that the r line makes with the horizontal. Note also that we know the distance "a", as the distance from the front wheel to the back wheel. A little bit of trig gets us:
r = a / sin(θ)
There's numerous simplifications here, but for sane values of a and θ they won't be noticeable.
Thanks, both of you. I have already looked at the more geometric approach -- but I aim (probably futile, but I will try) to have a realistic simulation based on physical properties.
I understand the basics (with trig and such), but the above diagram did help me understand the relationship between the two tyres. I'll read and try to understand more, thanks for giving me a starting point. Actually, Grade 11 physics probably has given me a base of understanding for some of this stuff, otherwise I'd be lost.
Thanks, again!
I understand the basics (with trig and such), but the above diagram did help me understand the relationship between the two tyres. I'll read and try to understand more, thanks for giving me a starting point. Actually, Grade 11 physics probably has given me a base of understanding for some of this stuff, otherwise I'd be lost.
Thanks, again!
Quote:Original post by solinent
Thanks, both of you. I have already looked at the more geometric approach -- but I aim (probably futile, but I will try) to have a realistic simulation based on physical properties.
The geometric approach is a prelude to a physical approach. Once you have the ideal r, you can calculate centripetal force. That lets you figure out whether there should be skidding or not. If you want you can skip all that and do a pure rigid body simulation, but if you're doing that you don't need to worry about all this stuff. Just set up your rigid bodies and your joints and simulate, and tweak constants.
Quote:Original post by SneftelQuote:Original post by solinent
Thanks, both of you. I have already looked at the more geometric approach -- but I aim (probably futile, but I will try) to have a realistic simulation based on physical properties.
The geometric approach is a prelude to a physical approach.
Yup - in particular you need to do the geometry in order to work out what angles the steering wheels will be at to eliminate slipping (the left/right wheels won't have the same angle).
Yeah, of course, I didn't intend to say that it wasn't a prelude, just that I have already considered it.
I think I'm going to have to rethink my entire car class before starting to code, now. Currently, it doesn't work very well.
I think I'm going to have to rethink my entire car class before starting to code, now. Currently, it doesn't work very well.
Alright, so I decided to get rid of turning until I got acceleration down right, so I decided to go directly into gears and gear ratios with RPMs.
All I require to know that I can't seem to find, is that when you accelerate, (lets say pedal to the ground constantly), is the increase in RPM linear? It isn't, obviously. So I come to the conclusion that with higher RPM's, there is less gear resistance (or is this overcoming static friction)?
Anyways, is this something very complicated, and I should simplify it, or is this something that I can accurately simulate? Is this rolling friction?
All I require to know that I can't seem to find, is that when you accelerate, (lets say pedal to the ground constantly), is the increase in RPM linear? It isn't, obviously. So I come to the conclusion that with higher RPM's, there is less gear resistance (or is this overcoming static friction)?
Anyways, is this something very complicated, and I should simplify it, or is this something that I can accurately simulate? Is this rolling friction?
Quote:Original post by solinent
All I require to know that I can't seem to find, is that when you accelerate, (lets say pedal to the ground constantly), is the increase in RPM linear? It isn't, obviously. So I come to the conclusion that with higher RPM's, there is less gear resistance (or is this overcoming static friction)?
Pushing the pedal towards the floor results in higher torque, translating to higher acceleration. RPM is a (proportional) measure of velocity when the clutch is engaged.
RPM increase within each gear is proportional to speed increase however what complicates matters is that the torque developed by an engine is normally some sort of curve over the entire RPM range and wind resistance increases (approximately) as a square of the velocity. Of course then there are a million other factors like.... blah blah blah. In the end we often fudge many of these factors!
How realistic do you want to go in this simulation? You can get pretty good results with a linearly reducing acceleration (full acceleration at zero mph and zero at max mph) and forgetting about torque and gear ratios etc.
When you get back to turning there are again different levels of realism and effort involved. So before I delve into any more detail I'd be interested in what you're trying to achieve, realism or arcade fun?
How realistic do you want to go in this simulation? You can get pretty good results with a linearly reducing acceleration (full acceleration at zero mph and zero at max mph) and forgetting about torque and gear ratios etc.
When you get back to turning there are again different levels of realism and effort involved. So before I delve into any more detail I'd be interested in what you're trying to achieve, realism or arcade fun?
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