rear springs part 1

I find surprisingly little about how to calculate spring rates when I read.  I thought about it and realized a few things

The amount of droop you have depends entirely on spring rate.  The sprung mass at the rear rests on the rear springs.  It doesn't matter if you have coil overs that allow you to dial the ride height up and down.  If you know your bump travel, then the load at full bump is determined already as well.

"Tune to win" recommended that for a beam axle car you want a minimum of 3 inches bump and 4 droop.  If you look at the travel on most inexpensive shock absorbers, the extended to compressed height is significantly less that 7 inches.  I conclude from this that the shocks will have to be run at an angle to the axle to get the needed travel as shown on this car:

I never knew why that was done before.  This means that spring rate decreases the further you displace, which is the opposite of what you would ideally want.

I also thought about the ratio of sprung to unsprung weight.  As you roll over a sudden bump the axle is accelerated upwards.  If the body of the car is light or the spring rate is high, the acceleration of the car body upwards is high.  I think there is a perception that this affects passenger comfort only.  It affects performance as well as it means the cars pitch is constantly changing which affects the suspension geometry, and causes the wheel loads to change dramatically.

If the wheel load is changing dramatically, then the cornering force that can be supported by the rear wheels is suddenly disappearing and reappearing.  We have all felt this when cornering in a empty Uhaul truck which has stiff springs.

All this is telling me that I need to have an idea of the sprung and unsprung weights of my car so that I can choose an appropriate travel, and spring rate.  I don't want to spend a lot to know this so I bought two bathrooms scales for $8 each.  I know a regular car weighs about 3200 lbs.  If half that is on the rear, then I have to support about 1600 lbs with two scales that go to 300 lb each.  This is easy to do with levers:

 

Where Fs is the force on the scale.  Fc is the weight of the car.  Fj is the force on the jack stand

 

I put the first side as shown and saw that the car was off both jacks and that the load was much lower than I was expecting.  So low that it would be below the scale limit if directly measured:

 

 198 lbf!  This seems impossibly light.  Add a battery (35 lbf), A fuel cell and gas (75lbf), 20 lbf for all the brackets yet to be done.  So about 330 lbs unsprung

 

Sprung mass:

200 lbf.  Add wheels, tires and spacers (75 lbf).  So 275 lbf total.

 

The shocks, springs, control arms, and drive shaft are partly sprung and partly unsprung.  If we neglect these for a minute we have 605 lbf for the rear weight.  I am concerned, but not surprised at how light the rear end is compared to the front, and concerned at how heavy the axle is compared to the car.