COM check for understanding

[dknowles67]

There have been so many posts on this, I thought I had the physics understood, but a recent post by Stan seemed to contradict what I thought I knew.

I understand that there are lots of forces acting on a PWD car as it rolls down the track, and it is hard to change one thing without affecting something else.

Part 1.
So hypothetically speaking, Let's say you had a block of pine with axles and wheels that weighed 0 oz, and a thin bar of some material the length of which equaled the car's width, and this bar weighed 5oz, and that you could put the bar anywhere on (in) the car you wanted. (the bar would go through the width of the car, parrallel to the axles, you could move it up/down, and front/back - trying to keep this in 2 dimensions)

The COM would be where you placed the bar.

Let's ignore losses from friction - assume a perfectly smooth track, perfect alignment, never hitting the rail, or any bumps.

Now let's contrain the PE - for comparing any two positions, the two positions must provide the same Potential Energy (the change in height must be the same).

If I understand Stan correctly, placing the bar higher on the car, closer to the center of rotation of the track, (which is some place in space several feet above the track, as I imagine) would reduce the loss in energy as the car rotates in the curve of the track, in comparison to a similar position further away from the center of rotation. (although this would be a very small savings in energy loss).

Part 2.
Again, if I understand Stan's post correctly, the real energy savings from a low COM comes from the rotation induced when hitting bumps in a track.
Each bump causes the car to rotate in one direction when the front wheels hit, and then in the other when the back wheels hit.
To me, this would imply it is better to have a COM concentrated exactly between the axles (ignoring all other factors) - in the axle plane.
A "barbell" designed car, with 1/2 the weight at the front end, and 1/2 at the rear end of the car would suffer the worst from this, as all the weight would rotate at the greatest distance from the center of rotation.

I realize in the real world, it would be nearly impossible to get the COM below the axle plane, and still meet the 3/8" clearance.
But if there were a way, would there be any advantage to having a lower COM?

My understanding is that on this forum, when we talk about a low COM, we mean as close to the axle plane as possible, not really as low as possible, except to the extent that they are one in the same.

I can't see where going lower than that would create any advantage.
Comments?

[Stan Pope]

I think you are okay on Part 1.

On the comment about "low as possible," I have taken CM below axle plane by maybe 1/8" or so. Doing so does increase the PE available slightly. Some loss for small bumps, some gains for large bumps.

[dknowles67]

Thanks.
Wow.
COM 1/8" below the axle plane.
I think I drill the axles 1/8" above the bottom of the block to give 1/8" all around the axle holes (and maintain 3/8" required clearance).
You must have got your COM right on the bottom of the car.
Thin plate maybe?
Screwed to the bottom?

[Teeeman]

I think you are okay on Part 1.

On the comment about "low as possible," I have taken CM below axle plane by maybe 1/8" or so. Doing so does increase the PE available slightly. Some loss for small bumps, some gains for large bumps.

You must slice your cars very, very thin!

Or you grip the axle with less than a full hole?





-Terry

[Stan Pope]

You must slice your cars very, very thin!

Or you grip the axle with less than a full hole?

Well, I've been accused of being a shovel full shy of a full hole! But I don't think that they meant anything about PWD!

Actual wood thickness of more than 2/3 of the car is 0.0000" +/-. Rest is very thin. Weight used to offset the neutral effect of wheels/axles.

[Teeeman]

(laughing!)

.000" thick... hmmm... sounds like a rail?


-Terry

[pinecarpro]

You can get a lot weight below the axles by using lead flashing.

Stan, is the PE you are talking about here the same force as a weight on a pendulum? Because that’s how I thought where to put weight and would explain in laymen’s terms

[Stan Pope]

You can get a lot weight below the axles by using lead flashing.

Stan, is the PE you are talking about here the same force as a weight on a pendulum? Because that’s how I thought where to put weight and would explain in laymen’s terms

The lower (in the car) the CM, the less it is rotated downward (relative to the track) as the car is rotated from level to 30 degr slope.

The pendulum model may apply, but the analogy is messy to establish.

[dknowles67]

I still feel like I have no answer to one of my original questions.
We've established that it is possible to get the COM below the axles.
Stan has stated that this increases the PE slightly, which I agree with.
The bottom back corner of the car will drop the furthest distance.
One of my original constraints was to keep the PE the same for any comparisons.
I'm also trying to keep this in 2 dimensions, by ignoring any left to right rotation caused by bumps.
Ignoring the increased PE, and exploring the possibility of getting the COM below the axle plane (let's even allow it to get below the track, for the sake of argument), is there any energy savings provided?

It seems to me that as you move away from the axle plane, in either direction (up or down), you increase the energy expended as the car goes over a bump, and rotates first in one direction, then in the opposite direction.
Maybe on a smooth track, the increased PE more than makes up for this. (unfortunately, we race on very old, wooden, bumpy tracks, comparatively speaking)

[Stan Pope]

I still feel like I have no answer to one of my original questions. ... Ignoring the increased PE, and exploring the possibility of getting the COM below the axle plane ... It seems to me that as you move away from the axle plane, in either direction (up or down), you increase the energy expended as the car goes over a bump

I think that you are trying to quantify the trade-off between energy gain and loss from lowering the CM.

You might start your quest by using some simple numbers like "what if the CM were lowered by 1/10th the distance from CM to rear axles?" That makes computations easier.

Now, you get to "earn the answer" by digging out the appropriate equations to estimate the results!

[dknowles67]

The problem lies not so much in my ability to

digging out the appropriate equations

But in the application of these equations to the physics of PWD cars.

The KE lost during the rotation would be = 1/2mr2w2.
The 1/2 and m (5oz) are fixed.
The w (angular velocity) would be the speed of rotation, and would be dependent on the speed the car was traveling, and the height of the bump I imagine, but could be held constant for comparison purposes.

The r (radius) part is what I'm focusing on.
We've stated that the car rotates about the COM, so it would seem r would be zero in these equations, no matter where the COM is, which doesn't make sense to me.

I guess I think the rotation caused by bumps in the track is NOT around the COM.
I think the rotation is first around the rear axles, and next around the front axles.
So a COM that was exactly between the axles would minimize the loss of KE due to bumps in the track.
Therefore, moving the COM above/below the axle plane would increase r, and thus increase the KE lost during the rotation (exponentially, since r is squared in this equation).
How's that for a theory?

[Stan Pope]

I guess I think the rotation caused by bumps in the track is NOT around the COM.
I think the rotation is first around the rear axles, and next around the front axles.

Yes!!!

So a COM that was exactly between the axles would minimize the loss of KE due to bumps in the track.
Therefore, moving the COM above/below the axle plane would increase r, and thus increase the KE lost during the rotation (exponentially, since r is squared in this equation).
How's that for a theory?

So far, so good.
Lowering CM below axle plane increases the impact energy losses.
Lowering CM below axle plane increases the PE available.

Next step is to compute the differences and find the transfer point.

[dknowles67]

Next step is to compute the differences and find the transfer point.

But that would not be possible, unless you knew how many bumps the car will hit on any particular run down the track.
I suppose you could come up with a statistical average, possibly based on empirical (measured) data.
I think you would find a different answer for a smooth track vs a bumpy one.

For a smooth track, the losses due to bumps would be small, thus allowing you to move the CM lower, and further back (closer to the point of maximum PE).

For a rough track, the losses due to bumps might be severe, and require moving the CM closer to the midpoint between axles, on the axle plane.

In other words, it doesn't do any good to maximize PE, if you use it all up on the way down.

It would be better to minimize the loss, and start with less.

That's why there's never a good answer to the old question - "Where do I put my COM?"

It always depends on the track.

Lowering CM below axle plane increases the impact energy losses.

I think this is the answer I was searching for.