How to Slow Down Faster: The Math behind Brakes. Part 4: Weight Transfer

brake2

Part 1 is here.

Part 2 is here.

Part 2b is here.

Part 3 is here.

     We’re almost done here.  Stay with me.  The last variable we have to plug in is weight transfer.  Last post we talked about front:rear weight ratio affecting an otherwise perfect brake balance between front and rear if the ratio was 50:50 and the front and rear brakes were the same.  But that’s almost never the case with cars.  Most with front engines are front heavy, and those with engines in the rear are obviously rear heavy.

     So how do we compensate for a front:rear weight ratio other than 50:50?  We make the brake proportions also the same ratio.  If the weight ratio is 60:40, then we make the brake ratio between the front and rear 60:40 to create a perfect brake balance.  Now that we’ve got that figured out, lets add in weight transfer.  As I said before, weight transfer is what you feel when you suddenly brake.  Your body flies foward, like something is pulling you that way.  That’s weight transfer.  The weight is moving from the rear to the front due to the deceleration.

     So far we’ve only talked about the brake system when the car isn’t moving, ie: its not decelerating.  There is no weight transfer.  If we factor in weight transfer, our front:rear weight ratio will change, reflecting how hard we’re declerating.  The problem now is that how hard we brake is never the same.  We might lightly brake if we’re driving around town, or brake hard if we’re on the track.  So if our static weight ratio is 60:40, our weight ratio under heavy braking might change to 80:20, but during street driving it might only be 70:30.  So how do we calculate for both situations while maintaining a perfect brake balance and the shortest stopping distance?

     Well, first to calculate Weight Transfer, we use this equation:

mathbrake4

      Here we need the Total Vehicle Weight, the Deceleration, the Center of Gravity Height, and the Wheelbase.  The last two you can find from the manufacturer, as well as the first one, but the second one is what complexes things.

     If you remember, Deceleration is our desired result from all the calculation.  It’s what tells us how well the car’s braking.  But if that’s out final result, then how do we plug it in in the middle of the process?  Well think about it.  If we want to know how much weight is being shifted, we have to know how hard the person’s braking right?  That’s why the front:rear weight ratio will always be different depending how hard we brake.  If we brake lightly, not much weight will be transferred, resuling in a totally different “perfect” brake balance (ie: 70:30 if our static is 60:40 )than if we brake hard, where more weight will be transferred (ie: 80:20).  So to figure out how much weight we’re shifting, we must know how hard we’re decelerating.

     So if we’re braking hard at say, .8 gs, the weight transfer will obviously be different than if we were braking at just .4 gs.  So if we were to plot this on a graph, as we increase our deceleration, our weight transfer will also increase.  And in return, the front:rear weight ratio will change, forcing us to change our brake balance again.  So how we achieve a perfect brake balance all the way through?  We use a proportioning valve.  We first set out brake balance so it first our maximum deceleration/maximum weight transfer, and then insert a proportioning valve.  The valve will adjust the brake balance so that as we brake harder, itll adjust the brake force towards the front.  Here is a before graph of Brake Balence vs Deceleration where the brake balance is tuned for the maximum brake force, forsaking the minimum and everything in between.  And here’s a graph with the prop valve in use.  You can see how the prop valve adjusts the brake force so that it applies just about the right amount of brakes to the front to keep the brake balance in place.

     I previously had you disregard the tire’s maximum Mu, but now we’ll also put that into consideration.  I promise that’s the last variable to consider.  The average all-season tire on dry tarmac can produce about .9 gs of deceleration.  So if your front brakes are producing 1.0gs with that tire, you can only stop at .9gs and that extra brake force will be wasted.  That’s why a balanced brake bias is so important; so as to not waste the extra brake force, and instead move it to either the front or back and maximize our deceleration grip.

     And that’s our last segment.  I’ll add in one more post, plugging in numbers for all of our variables, showing you one way to use these equations.  I’ll also add a few graphs later to show the deceleration to weight transfer graph.  Stay tuned.

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