World Record Run

[FatSebastian]

So I don't think I'd try for speed..

...perhaps it would help to design a slower car.

I think Whoda & Darin may be on to something. As far as I can tell, the track appears to be mostly downhill. As the drop (h) increases, so does its speed (v)



Thus, with the starting line very high, these cars are reaching speeds at which ramp defects become perilous. I like Stan's suggestion of weighted wheels. It stores the energy into rotational momentum (like four flywheels) and thus regulates the car's linear velocity down the ramp. It also has the potential to better maintain speed through the level area near the end.

The extra performance usually gained by an aft CoM placement seems negligible given the excessive height of the ramp. I would also agree to keep the CoM in the middle and align to run with minimal toe.

[FatSebastian]

Thinking more about this, it would be an interesting exercise to design an extremely long track that better accommodates conventional derby-car designs. One approach might be to have a typical start section of 4' drop over ~12', followed by a straightaway with a grade just shallow enough to overcome rolling friction and keep the cars moving at typical derby speeds.

(If the track was long enough, and the number of participants great enough, multiple races might be run simultaneously on a well-designed track - as long as no cars got stuck!)

So how would one determine the proper grade of the straightaway? What about alternatives to plywood? Other track-design ideas?

[Stan Pope]

(If the track was long enough, and the number of participants great enough, multiple races might be run simultaneously on a well-designed track - as long as no cars got stuck!)

Timer management might be a bit tricky!

And would need a squad ... no, a regiment ... of helpers stationed along the track to "rescue" really slow and/or stopped cars. However, a rescue of a slow car could be problematic because if it is still rolling, it might have ended up being the only car of the day to finish its heat!

[Stan Pope]

Thinking more about this, it would be an interesting exercise to design an extremely long track that better accommodates conventional derby-car designs. One approach might be to have a typical start section of 4' drop over ~12', followed by a straightaway with a grade just shallow enough to overcome rolling friction and keep the cars moving at typical derby speeds.

Interesting idea, but doomed from the outset, I think. Here's why:

Suppose the slope is set so that the car with the best "composite coasting friction" holds its speed. The cars with lesser frictions will stop before reaching the end of the track.

On the other hand, suppose the slope is set so that a car with a lesser "composite coasting friction" holds its speed. Lesser cars will suffer as before but better cars will continue to get acceleration from the track slope.

Here's why I think that is wrong:
If the slope is set so that a lesser car just holds its speed, better cars will accelerate to faster speeds on the slope. They will have a limiting speed that is dictated by their aerodynamic friction which increases with speed.

The question is whether a car can be built with sufficiently low aerodynamic friction that its limiting speed is unsafe. That would "break" the track design concept.

[FatSebastian]

Interesting idea, but doomed from the outset, I think.

Here's why I think that is wrong:

This reply confused me a little, as it began predicting doom but then suggested that forecast may be wrong.

The force of gravity pushing straight down on the car should be m*g, where m ~ 5 ounces and g ~ 32.2 ft/sec^2. If I understand so-called free-body diagrams, the force pushing the car down a ramp of constant slope theta will be F = m*g*sin(theta). Thus, if one had a reliable estimate the total drag/friction force F of a car at speed, would not a suitable grade be estimated as theta > arcsin(F/(m*g))?

The cars with lesser frictions will stop before reaching the end of the track.

If one is designing a world-record track, then a loftly goal would be to get "typical" PWD car-designs to survive the trip down the track. Any car that has problems barely getting down the local Pack's track should be assumed to also have problems on a world-record track. Likewise, any car that is above average on a normal track should hopefully survive a well-designed long track as well. Thus I think a design might favor lower friction cars over high-friction cars, and it would seem like an easy thing to put a temporary air-drag device on an existing super-low-friction car to regulate its speed for survival, if necessary.

That would "break" the track design concept.

Assembling a steep ramp on a convenient hill side already seems like a "broken" track-design concept, given that only three cars actually finished, so I wonder about alternatives that might be "less broken"!

[FatSebastian]

Timer management might be a bit tricky!

A timer may not be necessary. After several hundred feet, the probably of near-ties might be low enough that line judges / video stills can be used.

And would need a squad ... no, a regiment ... of helpers stationed along the track to "rescue" really slow and/or stopped cars.

I wonder if it might be possible to just create a heavy "box" on wheels that spans all lanes and with a shallow ramp on the front that either pushes the stuck cars the rest of the way down, or rolls up under them and catches / collects them.

[Stan Pope]

This reply confused me a little ...

After I pushed the "post" button, I wondered if it would create confusion, especially with FS. But I thought, "No ... he'll get it."

The sequence reflects the evolution of the thought about friction, beginning with friction dependent on wheel CoF, which is independent of speed, and then recognizing the involvement of friction components which are dependent on speed, which will prevent runaway acceleration. Absent such components, the car would keep accelerating until it broke the sound barrier (if the "flat" were long enough.)

[Stan Pope]

... Thus, if one had a reliable estimate the total drag/friction force F of a car at speed, would not a suitable grade be estimated as theta > arcsin(F/(m*g))?

That looks like a good formula! If only we knew the F for "composite coasting friction" of a typically slow car. As we know, it will be a function of V (speed) and d (drag coefficient) and Af (cross section) as well as rolling friction for the wheels and slicing friction for the axle-hub interface.

Then you should also be able to compute the speed of an ideal car at various points on the track. How long must that track be for that ideal car to go supersonic?

[FatSebastian]

If only we knew the F for "composite coasting friction" of a typically slow car. [...] Then you should also be able to compute the speed of an ideal car at various points on the track.

I would be tempted to approach the problem in reverse fashion, say, by repositioning a timer's "electric eyes" at various points along one lane of a level track (i.e., the sensors of 4-lane timer can measure 4 points along a single lane). Conceptually, measuring the differences in time between each point provides an estimate of average speed, and changes in average speed would yield the deceleration. (In practice, one would repeatedly run the experiment to average out the noise, and then collect the data into "equations of condition" in a "least-squares" estimation problem and solve the normal equations directly for the deceleration term.) Multiply the deceleration by the mass to get the force F. Of course, before building the apparatus, a sensitivity analysis would need to be performed first to find out how accurately such an experiment could work given errors in the sensor locations, lack of level, timer precision, etc., but in principle it seems possible. I don't know of a better or easier way to determine F without, say, a wind tunnel.

[Stan Pope]

Yup! Should work.

You gonna cut up your FastTrack Timer? Or build one with an Arduino?

If you build, you don't have to worry about a start-gate trigger ... just start the timing based on the trigger of the first gate on the flat. Wonder how many split points an Arduino could time accurately? 7 gates would give you 6 intervals of data to work with.

[bracketracer]

Yup! Should work.

You gonna cut up your FastTrack Timer? Or build one with an Arduino?

If you build, you don't have to worry about a start-gate trigger ... just start the timing based on the trigger of the first gate on the flat. Wonder how many split points an Arduino could time accurately? 7 gates would give you 6 intervals of data to work with.

I know an Arduino Uno can work for six sensors. I built the one from the http://www.miscjunk.org website (plans are here: http://www.miscjunk.org/mj/pg_pdt.html ). I use it on a two lane Besttrack with one sensor at the left lane's finish and six sensors in the right lane. The left lane's sensor and the fifth sensor in the right lane use the same pins on the Uno, I wired in a DPDT toggle to select which sensor is active. I detailed the build here: http://www.pinewoodderbyonline.com/post ... er-6952101

[whodathunkit]

Dunno what the world record rules are ... but for about the same money, they could have had a 1200' 2-lane track ... almost 1/4 mile. A good time could be up around a minute.

Stan, I think you thinking on this is right on track !

There is a topic here on DT ..
With a world record track back from 2010 where it took the cars about 20 sec to go 263 feet.

[Stan Pope]

Since we are trying to determine coefficients experimentally, it would make sense to start with a model formula that reflects the speed decay. This would include coefficients relating to rolling friction, bore-hub friction, aerodynamic drag, DFW friction against rail and track, inertia, etc. Then, rather than speed traps at various points along the track, one could place sensors spaced regularly along the track's coasting area, collect data (time at which the car passed each sensor) with the car starting at various heights along the ramp (to cause the car to coast at different speeds), then perform a least squares curve fit of the collected data to the model formula. (Should not have to record the starting heights!)

Since it is a physical process with few uncontrolled variables, the correlation should be excellent and accuracy of the deduced coefficients should be good.

This is a way to "back into" a measurement of the drag coefficient for various car designs!

Note 1: Track set-up should be meticulous so as to avoid disturbance from track section transitions.
Note 2: Some arrangement to get speeds above the normal for the track's starting line height should be implemented. Alternatives include (1) extending the ramp, (2) giving the car a nudge forward when releasing it and (3) putting blocks under the ramp support to raise the ramp.

[FatSebastian]

Since we are trying to determine coefficients experimentally, it would make sense to start with a model formula that reflects the speed decay.

Personally, I was only proposing to estimate overall deceleration for the purpose of laying out a gradually sloping track that won’t throw cars easily. For that task, individual performance parameters seems more than necessary.

Rather, I suspect it might be enough to represent the location of the car along the test track flat (ri) as a Taylor series expansion:

ri = r0 + v0 (ti – t0) + ½ a0 (ti – t0)² + … (neglected higher order terms), i = 1, 2, …

where r0 is the location of the initial sensor, v0 is the speed at the initial sensor, a0 is the acceleration (assumed constant if higher order terms can be neglected), and (ti – t0) is relative timer outcome between the initial sensor and the ith sensor. As Stan suggests, one can simply define all distances and times relative to r0 and t0, making those terms effectively zero by convention. Thus, given ti as observations and ri as physically measured constants, there are two unknowns (v0 & a0) remaining to be solved for.

This model seemingly requires only three sensors to provide a solution. In reality, the model is imperfect and there will be other sources of random error, so readings from more than the three sensors would improve the estimate if combined in least-squares fashion. Once a0 is estimated, then the total frictional force can be calculated as F = m a0, where m is the mass of the car. From that, a track slope might be inferred which hopefully keeps cars moving at a fairly reasonable pace.

[Stan Pope]

I think that you are right, FS. I was stepping a bit past the goal that you expressed with a recognition that the method could measure factors that are difficult to measure otherwise... "standing on your shoulders", so to speak. Thank you.