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!

[flyerncle]

Interesting read and makes a lot of sense,what effect does spring length make.

[alga]

All things being equal, spring length changes the ride height, but since the ride height is adjustable anyway, there should be no difference as long as it's in the right ballpark. All my springs are 8" long, and with the softer springs the adjusters are close to the middle of the thread front and back.

I set up the ride heights by piling 4 wheels with tyres on the driver's seat, and then getting all 4 lower wishbones level. Seems to have worked OK, but I plan to get the corner weights balanced at some point.

[flyerncle]

Used shorter heavier springs (ie 350/250) on the Haynes I built to race for someone and it had very pronounced oversteer,it had Ginetta rear uprights that are are direct fit for the Haynes and same dims and Protech shocks with the springs as stated,just too much of a racing car for the pilot.

[baz-r]

I think that something is going on wrong herei can't seem to get the same workings out when I calculated it off my car (Sierra based)
To get the ratio of 1:1 in the rear then the shock and spring would need to be vertical?
The suspension tec guy who gave me the equation to use after I had my sprung and unsprung weights calculated said to simply measure the difference in ratio between the change in short planks against the distance Moved by The Hub centre height giving you a true shock ratio
I was pretty close to my estimated figures with my car finished
350 is pretty good on the front end and I increase the back to 260 and its not over firm and handling is pretty balanced

[Ianr]

I went 350/250 on mine but found that whilst it was perfect one up it needed a bit more for bumpy roads in north Norfolk so went to 350/300 which worked fine (My passenger was over 6'3" and I'm over 6' so smaller lighter passengers will probably be better with your 260 rears)