Calculating ride frequency for the Mustang

[Järn]

Chart updated Aug. 25, 2020

I am working on a simple Google Sheets calculator for ride frequency. I found a simple formula here:
https://www.drtuned.com/tech-ramblings/2017/10/2/spring-rates-suspension-frequencies
http://downloads.optimumg.com/Technical_Papers/Springs&Dampers_Tech_Tip_1.pdf

f (Hz) = 1/(2Pi) x SqRoot(K/M ) where K = spring rate (N/m) divided by M = mass (kg)

Notes: Mustang GT non-PP, front spring calculation total weight = 3705 lbs, front = 53% or 1964 lbs, base spring= 160 f/lb, 1 lbs/in is equal to 175.126835 newton/meter. lbs to Kg = 0.453592

k = 160 lb/inch * 175.126835 = 28895.927775 N/m
m = 1964 lbs (front axle) / 2 (corner) * 0.453592 = 445.5 kg
k/m = 28895.927775/445.5 = 64.86179
1/(2Pi) = 0.15915494309 note: 2Pi = 6.28318530718
√64.86179 = 8.0536817667
0.15915494309 * 8.0536817667 = 1.28 Hz Front Springs

Rear Springs: 668 lbs/inch = Frequency of 2.74 Hz

Using the online calculator with a Motion Ratio of 1 my numbers match the online calculator.

Question: How do I reconcile the Front and Rear Ratios? 1.28Hz and 2.74 Hz
I ask because I see references to categories like this. Are these categories just for front axle/springs?

0.5-1.0Hz Passenger cars, typical OEM
1.0-1.5Hz Typical lowering springs
1.5-2.0Hz Rally Cars
1.5-2.5Hz Non-Aero racecars, moderate downforce Formula cars
2.5-3.5Hz Moderate downforce racecars with up to 50% total weight in max downforce capability
3.5-5.0+Hz High downforce racecars with more than 50% of their weight in max downforce

Standard Road Car: < 1.3 Hz
Sporty Road Car ("ST- Versions"): 1.3 Hz - 1.5 Hz
Very Sporty Road Car ("RS-Versions"): 1.5 Hz - 1.8 Hz
Super Sports Car (Ferrari, Lambo etc): 1.7 Hz - 2.0 Hz
Rally Car in Tarmac Setup 2.2 Hz - 2.6 Hz



Thank you...

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[Norm Peterson]

Couple of comments . . .

I've been running these calculations since before Google, so I'm going to have to check that site out. Well-intended online calculators don't always consider everything that is involved.

Don't forget to deduct the unsprung corner weights. Ride frequencies will go up a tad.

The motion ratios are unlikely to be 1.0 in most cases other than with a live axle that sits the springs on the axle proper. MacPherson strut motion ratios are typically 0.97-ish, which makes the wheel rate around 0.95 times the spring's rate.

Interesting to see a breakdown made in terms of aero downforce. Thanks.


Norm

 

[Norm Peterson]

He should have made more things variable, like frequency and motion ratio in particular.


As a side note, once you introduce damping (shock & strut effects), the ride frequency drops. Not by much at first, but as you get up to, say, 50% critical damping, the actual frequency could be nearly 15% lower than what the theoretical undamped vibration calculations give you. 50% critical damping is fairly firm damping.


Norm

 

[Brian@BMVK]

I am working on a simple Google Sheets calculator for ride frequency. I found a simple formula here:
https://www.drtuned.com/tech-ramblings/2017/10/2/spring-rates-suspension-frequencies
http://downloads.optimumg.com/Technical_Papers/Springs&Dampers_Tech_Tip_1.pdf

f (Hz) = 1/(2Pi) x SqRoot(K/M ) where K = spring rate (N/m) divided by M = mass (kg)

Notes: Mustang GT non-PP, front spring calculation total weight = 3705 lbs, front = 53% or 1964 lbs, base spring= 160 f/lb, 1 lbs/in is equal to 175.126835 newton/meter. lbs to Kg = 0.453592

k = 160 lb/inch * 175.126835 = 28895.927775 N/m
m = 1964 lbs (front axle) / 2 (corner) * 0.453592 = 445.5 kg
k/m = 28895.927775/445.5 = 64.86179
1/(2Pi) = 0.15915494309 note: 2Pi = 6.28318530718
√64.86179 = 8.0536817667
0.15915494309 * 8.0536817667 = 1.28 Hz Front Springs

Rear Springs: 668 lbs/inch = Frequency of 2.74 Hz

Using the online calculator with a Motion Ratio of 1 my numbers match the online calculator.

Question: How do I reconcile the Front and Rear Ratios? 1.28Hz and 2.74 Hz
I ask because I see references to categories like this. Are these categories just for front axle/springs?

0.5-1.0Hz Passenger cars, typical OEM
1.0-1.5Hz Typical lowering springs
1.5-2.0Hz Rally Cars
1.5-2.5Hz Non-Aero racecars, moderate downforce Formula cars
2.5-3.5Hz Moderate downforce racecars with up to 50% total weight in max downforce capability
3.5-5.0+Hz High downforce racecars with more than 50% of their weight in max downforce



Thank you...

You have to factor in the motion ratios of the suspension to get that correct. Also the mass should be based on the sprung mass not total mass.

 

[Dana Pants]

Here some screenshots from my phone that hopefully make it more clear.

 

[Järn]

You guys are the best! wheel rate = (Spring rate) * (Motion ratio)^2

I just did some popular linear springs. I am going on a little vacation, I can add more next week.

 

[Dana Pants]

If your goal is perf, you just buy the stiffest lowering springs and trust us that it’s not really that stiff compared to what someone would do with coil overs.

And you balance any issues with a swaybar afterwards.

 

[shogun32]

=187.8*SQRT(H33/((LF_sprung+RF_sprung)/2))/60

I took Brian's spreadsheet and converted it all to formulas instead of static values.
https://www.dropbox.com/s/yytkee6jlsmvofj/S550 Mustang Springs.xlsx?dl=0

 

[shogun32]

If your goal is perf, you just buy the stiffest lowering springs

I disagree. Buy the softest spring and preload combination that results in the desired amount of static ride height AND pitch moment (ak suspension travel) under weight transfer. Then your suspension can actually work properly. Now if your suspension is crap, soft springs will highlight it's crappiness vs masking it with high rate springs which is what these cut-rate coilover guys resort to.

Now I don't know what spring rate is the answer to the above but the consensus of a variety of spring+damper combos seems to point to 200-250F and 800-1000R with 225/900 being a good place to start.

My GT has the Steeda dual-rate and IMO that's definitely most appropriate for full time track use and a bit much for street use, but liveable.

 

[Dana Pants]

I disagree. Buy the softest spring and preload combination that results in the desired amount of static ride height and pitch moment (ak suspension travel) on weight transfer. Then your suspension can actually work properly. Now if your suspension is crap, soft springs will highlight it's crappiness vs masking it with high rate springs which is what these cut-rate coilover guys resort to.

Now I don't know what spring rate is the answer to the above but the consensus of a variety of spring+damper combos seems to point to 200-250F and 800-1000R with 225/900 being a good place to start.

250 front isn’t sufficient for corner killing with big wheels and camber. It’s just the stiffest spring that can fit in the stock shock geometry without falling out.

 

[shogun32]

250 front isn’t sufficient for corner killing with big wheels and camber. It’s just the stiffest spring that can fit in the stock shock geometry without falling out.

that's an artifact of whomever created the other springs and being sized 'wrong'. If the right spring rate is not available in the correct length so it'll stay put and under compression at extreme travel, have a heart to heart with the manufacturer or insert spacers sufficient to fix the problem.

For example, Steeda's coilover takes a 2.5" spring that's too short at full droop so they provide a helper spring. I find that solution to be sub-par. If I can't source a spring that is of sufficient length to keep properly preloaded, then I'll whip up a spacer.

 

[Brian@BMVK]

250 front isn’t sufficient for corner killing with big wheels and camber. It’s just the stiffest spring that can fit in the stock shock geometry without falling out.

This is true. It's a pretty stout dual purpose setup though.

 

[Radiation Joe]

that's an artifact of whomever created the 250 spring in question and it being sized 'wrong'. If the right spring rate is not available in the correct length so it'll stay put and under compression at extreme travel, have a heart to heart with the manufacturer or insert spacers sufficient to fix the problem.

For example, Steeda's coilover takes a 2.5" spring that's too short at full droop so they provide a helper spring. I find that solution to be sub-par. If I can't source a spring that is of sufficient length to keep properly preloaded, then I'll whip up a spacer.

I disagree. With stock geometry struts we're limited to 250 lbs/inch or they'll fall out. Shortened struts and shocks are necessary to run acceptably effective springs for track use. With porky cars such as ours that means 400 to 600 lbs/in depending on how sticky of tires we're running to stay off the bump stops under late braking maneuvers and curb hopping. Same applies to the rear suspension. That's why you see so many setups with wheel rates in front 50 percent higher than in the rear ... weight transfer under braking is much more significant than under acceleration.

 

[NightmareMoon]

OP didn't say why he wanted to calculate the ride frequency, so lets not get too sidetracked as to which spring is 'best', mmk? Ride frequency is just a data point.

 

[Radiation Joe]

For an example of what I believe is a proper track rat set-up (you've got to pay to play...) is the Vorshlag MCS spring shock combo.

• Front Spring Package includes a pair of Hyperco 60mm ID Coilover Springs. These can work with the included MCS upper spring perches or the optional Vorshlag camber/caster plates and radial bearing upper spring perches

• Rear Spring Package, coilover: includes a pair of Hyperco 2.25" ID Coilover Springs and MCS upper spring perches, and Vorshlag upper shock mounts.

• Vorshlag's GT Spring Package is 450 #/in Front / 550 #/in Rear
• Vorshlag's GTS Spring Package is 600 #/in Front / 750 #/in Rear
• Vorshlag's GTR Spring Package is 800 #/in Front / 1100 #/in Rear

Ground Control doesn't list spring rates on their web store but if the BMW rates I'm familiar with are indicative they'd probably be recommending spring rates similar to Vorshlag for competitive track use.

I guess my point is that 250 lb/in rates are a compromise based upon shock and strut geometries. Truly effective spring combinations for track use with sticky tires are generally twice as high.

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