Spring rates

[alga]

So I dug online a bit and found some info on spring rates and their tuning. Turns out, the rate of springs for an application is measured in their resonant frequency, which is proportional to the square root of (spring rate / corner sprung weight).

The book recommends 350 lb/in front and 200 lb/in rear springs, but AndyH found that the rear is too soft as the car was prone to understeer, and suggested hardening the rear to 250 lb/in.

After measuring and estimating some numbers for my car, I discovered that the resonant frequencies for the recommended 350/250 lb/in springs are 2.55 Hz and 2.44 Hz respectively. For a general idea, road cars have 0.5-1.0 Hz, sport suspensions are 1.0-2.0 Hz, 2.0-3.0 are track cars with no downforce, and frequencies above are only used with serious aero. In other words, our roadsters' suspensions are well into the track territory, which does not make sense for cars with soft seats and padded interiors!

So, I bought a set of 200 lb/in springs and installed then at the back, and moved the 250's to the front. With these springs my calculated frequencies are 2.15 Hz and 2.19 Hz. Still very sporty! However, now the rear spring rate is 80% of the front, whereas it was 71%, so the balance shifts to more oversteer/less understeer.

I've tested the car on a couple of autosolo practice sessions and competitions, and I have to report that it handles much, much nicer. The reactions are somewhat slower, there is more body roll and the rear is a lot looser and more controllable. It's become a bit closer in feel to a well sorted MX-5 from the brutal monster with razor-sharp reactions that it is.

Now, my calculations:

The main formula is:

187.8 * sqrt(wheel rate [lb/in] / sprung weight[lb]) = frequency [cycles per minute]

For the sprung weights, I assumed (IIRC) a weight of 624 kg with driver, 46% front, 54% back distribution, and unsprung weights of 36 kg at each corner (20 kg brakes, dampers, wishbones, 16 kg wheels).

Front:
Arm length (1451-494)/2 = 478
Arm length to damper 300
Angle 42.9 deg
So, with 350 lb/in springs, the wheel rate is

>>> 350 * 300/478. * cos(42.9/180*pi)
160.91423508927775

So, front leverage ratio is 0.46
Sprung weight 110 kg, 242.5 lb
Freq 187.8 * (161./242)**0.5 / 60 = 2.55 Hz

Back:
Damper acts directly on the rear upright, so there is 1:1 leverage there (give or take)
Angle 45.1 deg
So with 250 lb/in springs the wheel rate is:

Wheel rate
>>> 250 * 1 * cos(45.1/180*pi)
176.46789266967022 lb/in
Ratio 0.706

Sprung weight 131 kg, 288 lb
Freq 187.8 * (176./288)**0.5 / 60 = 2.44 Hz


TLDR: the book spring rates are for hardcore track use. If you want to enjoy the car on the road more, use softer springs!