I need a general rule of thumb or simple formula to determine the minimum radiius required for an experiment. I have a 2.4GHz remote control car that reaches about 45 mph. If I begin at a certain distance from the loop at ground level, how large will that loop need to be? The car measures 19" long.
Welcome to PF; You mean you want the max radius of the loop that the car will get all the way around? Rule of thumb - try: d<v^2/20 where v is the max speed on the horizontal and d is the diameter of the loop. This guarantees that there is enough KE at the bottom of the loop to make it to the top ... this size is smaller than the maximum you can get away with because it does not account for the car being under power all the way around. 45mph is about 20m/s so a diameter less than 10m? ... There are better calculations you can do.
Thanks. I did mean "minimum" because I don't want to have to build it larger than required...but I do understand that too large would not work. I'm doing a science experiment for my 6th. Grade class, and I'm going to vary speed, weight, tires,etc
d<v^2/20 gives d<20m if v=20m/s. if we assume that the car can maintain 20m/s all the way around the loop then the max diameter of the loop is determined by the centrifugal acceleration. The calculation is then d < 2*v^{2}/9.8 ≈ 82m The real solution is somewhere in between, so the max diameter of the loop is somewhere between 20m and 82m which is probably much too big for a school project. It might be better to decide what is a practical size loop you can build and see if we can predict the minimum speed required to make it around the loop. Is the RC model a F1 type race car? It is claimed that a F1 car has so much down force that it could drive upside down in a tunnel due to the suction created. It might be interesting to recreate that with a model.
I agree. The minimum loop size will depend on the dimensions of the car - i.e. the front and rear bumpers must clear the track. Since this is a school project, you should really relate the thing to something learned in school shouldn't you? Or is it extended research?
I don't think it is an F1". It's a Traxxas 4x4 model. I can't build a loop de loop larger than about 3', so I am limited. Varying the speed to see the results sounds good. If 3' will not be large enough, I think I need to scrap this idea. Thanks again.
It's not related to anything in school right now, just that I'm really into cars and the teacher wants us to pick something that interests us... Wheel base is 12 1/2" center to center and overall with bumpers is 22".
The usual one is to gravity feed cars into the loop - you can see how the initial ramp height compares with the loop height. If you can control the speed of your car, you can just run it slower. If it takes a bit to reach top speed you can find minimum run-up distance to loop the loop. The main issue is just that the car has to be able to fit on the loop. A 3' diameter may be a bit tight. How about building a ramp and working out the farthest you can get the car to jump?
There is a lot of overhang on that car! To make sure it will fit on a 3' loop without catching the bumpers, scratch out an arc on the ground using an 18" piece of string, lay the car on its side with the wheels touching the arc and check the bumpers do not touch the arc. We could of course do it mathematically, but we would need the diameter of the wheels and the clearance height of the bumpers together with the measurements you have already given us. For the physics, there is potential energy, kinetic energy, centrifugal/centripetal force, rolling and air resistance, etc.
If the car has a suspension, then suspension compression needs to be taken into account in order to make sure everything clears while experiencing maximum force, which will occur at the bottom of a circular loop. You could try making something like a clothoid loop or constant g loop, but that would be difficult.