**The Mark Ortiz Automotive**

**CHASSIS NEWSLETTER**

**Presented free of charge as a service**

**to the Motorsports Community**

**August 2012**

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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: markortizauto@windstream.net. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.

**GAS SPRING FORCE AND RATE
IN SHOCKS**

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*I was wondering what your
thoughts are on the tuning of Bilstein monotube dampers using the gas charge
pressure?
We are running northeastern style DIRT style modifieds with very soft spring
rates typically: LF 225 lb/in, RF 175 lb/in, LR 156 lb/in (calculated at static
ride for torsion bar), RR 171 lb/in (calculated at static ride for torsion
bar). Beam axle front and rear.
What I think I know:
Stock Bilsteins (non-rebuildable) are charged with 150 psi nitrogen from the factory.*

The Bilstein rebuild manual I have recommends 180 psi minimum nitrogen charging
after rebuild.

The lift force is strictly a function of piston rod area due to the area
difference between the rod side versus the non-rod side of the piston.

The lift force will increase at some rate as the piston rod enters the shock
body in bump displacing an amount of oil equivalent to the rod volume which
will cause the free piston to compress the gas charge therefore increasing the
rod lift force by a small amount. This depends a great deal on the free
piston area and the volume of the gas chamber.

Gas pressure increases due to heat build up of the gas charge during operation
although for short runs not a great deal.

A 14mm shaft damper will have approximately 43 lbs of lift force fully extended
with a 180 psi gas charge.

A typical starting point for valving is: LF&RF 162/55 @ Bilstein’s rating
of 10 in./sec and LR & RR 208/72.

The shocks have a 46mm bore. The fronts have a 7” stroke and the rears are 9”.

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*We are not allowed to use
externally adjustable shocks.
The tuning range used currently range from a low of 80 psi to a high of 175
psi. This seems low to me considering the recommended factory charge
starts at 180 psi.
At what point would you expect cavitation to start to occur?
How do you incorporate the shaft lift force into the overall spring rate at the
corner of a car?
What are your thoughts on tuning with gas pressures in general?
Do you feel the pressures I have quoted to on the low side? (They are
included on a recommended set up sheet provided by a Bilstein representative).
Do you consider the rod lift force an additional form of spring rate?
(The fronts are coil over units while the rears act very close to the torsion
arm contact point i.e. the motion ratio is very close to identical of that for
the springing)
What is the effect of oil column pressure on valving operation if any?
Thanks in advance for any insights you can provide.*

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First of all, it’s important
not to confuse spring force with spring rate. When we measure gas force in a
shock, that is not the rate of the gas spring. It is the force exerted by that
spring at a particular displacement value, or point in the shock’s travel. The
__rate__ of the gas spring is the amount per unit of displacement (per inch
of travel, using English units) that the force __changes__:* *it is the
first derivative of the force with respect to displacement.

The gas spring force at full extension can be considered a preload on the gas spring.

The rate will be a much smaller number, and it will not be a constant. The rate will rise as we compress the shock. If the gas volume is small and the shaft is large, we get more non-linearity, especially near full compression. However, for shocks of the dimensions the questioner describes, the rate is fairly close to linear over most of the travel, and it is small – on the order of 2 to 15 lb/in. We have a very soft spring here, with lots of preload. When the ride spring is also soft, the gas spring force will affect ride height noticeably, but it will add only a little to the overall wheel rate.

We can measure the rate of the gas spring on the car, in most cases – or at least, we can measure a good approximation of it. Since the gas spring is somewhat non-linear, the rate is never the same over any interval of displacement. However, the rate does not change suddenly and dramatically, so

we can measure force change over an inch of travel, and that will give us a very close approximation of the instantaneous rate at the midpoint of that interval.

With most suspensions, we can remove or disconnect the ride springs and anti-roll bars (if present), while leaving the shocks connected, and the suspension will still hold the wheels in place, although it won’t hold the car up. We can then support the car’s frame on jacks, at whatever ride height we want, with scales under the wheels. If we do this at just one end of the car at a time, we can use the brakes to keep the car from moving around, or chock the wheels at the opposite end of the car.

We can use scissor jacks or jack stands to support the car about half an inch lower than normal ride height, or a chosen estimated running ride height. We then raise the car an inch using hydraulic floor jacks, or a lift if we have one. We note how much the shocks travel in that inch of suspension movement. That closely approximates the instantaneous shock-to-wheel motion ratio at the midpoint of the travel interval.

We note the reading on the wheel scales. This will be the sum of the unsprung weight as acted on by gravity (not quite the same as unsprung inertia mass, but close to it for simple suspensions) plus wheel load due to gas spring force.

We let the car down onto the
jack stands or scissor jacks, and immediately note the __change__ in wheel
load. This will be a close approximation of the wheel rate of the gas spring
at the midpoint of the travel interval. The rate of the gas spring at the
shock will be that number, divided by the square of the motion ratio.

This works for coilover or strut suspensions, or any other design where we can remove the spring, leave the shock installed, and still have the rest of the suspension operational. It is necessary when we cannot remove or disconnect the shock without also removing or disconnecting the spring.

For most leaf spring
suspensions, the rear suspensions on most sprint cars, or any system where the
spring or torsion bar arm serves as a suspension member, we have to use a
different technique. We can’t remove the spring in such cases, but we can
generally remove or disconnect the shock. So what we do is measure wheel load
at both ends of a measured travel interval, with and without the shock, and
compare the amount of load __change__ with and without the shock.

In a big-spring stock car, or any case where the spring neither mounts on the shock nor acts as a suspension member, we can use either method.

We can also calculate the gas spring force change over a displacement interval, if we know the shaft diameter, the gas chamber/separator piston diameter, and the pressure at the beginning or end of the displacement interval we are considering.

It is best to model the compression as adiabatic compression, rather than constant-temperature. Some readers may not be familiar with the difference, so I will briefly explain.

If a body of gas is maintained at a constant temperature, and compressed to a smaller volume, the absolute pressure (pressure relative to total vacuum, or gauge pressure plus roughly 14.7 psi atmospheric pressure) is inversely proportional to the volume.

P_{1}
= P_{0} (V_{0} / V_{1})
(1a)

where:

P_{0}
= absolute pressure before compression, psi

P_{1}
= absolute pressure after compression, psi

V_{0}
= volume before compression

V_{1}
= volume after compression

Or, using gauge pressure, with English units:

P_{1}
= (P_{0} + 14.7) (V_{0} / V_{1}) – 14.7 (1b)

However, when we compress a gas, it doesn’t stay at constant temperature. It gets hotter from the compression, and the temperature rise exaggerates the pressure increase. If we let the gas sit long enough to cool to its previous temperature, we get the pressure given in Equation (1a) or (1b). But when a shock is in operation, there normally isn’t time for that to happen. The behavior is better approximated as adiabatic compression: compression where no heat is lost from or added to the system.

In adiabatic compression, the absolute pressure after compression is inversely proportional to the volume ratio raised to the power of 1.4, which is called the adiabatic exponent.

P_{1} = (P_{0} + 14.7) (V_{0} / V_{1})^{1.4}
– 14.7 (2)

A shock with a 46mm gas chamber and a 14mm shaft has a shaft cross-sectional area a bit less than a tenth of the separator piston area, so the separator piston moves about a tenth of an inch for each inch the shock compresses, or a little less. If the gas chamber is one inch long at half an inch extension from static length, it will be about 0.9” long at half an inch compression from static length, and its pressure will increase about 15%. That will increase the shaft force by the same 15%. If the shaft force is around 50 lb before compression, it is then around 58 lb after compression, for a spring rate of 8 lb/in.

If we cut the pressure in half, we get around 4 lb/in. If we double it, we get around 16 lb/in. If we double the size of the gas chamber, that roughly cuts the rate in half.

So there is an effect from changing the gas spring pressure, but it is small in terms of spring rate. It is bigger in terms of ride height, but we can adjust that on a race car. It will have an effect on ride heights and wheel loads if we set up the car with the shocks disconnected. I do not recommend doing that when the shocks have significant gas spring effect.

One advantage of having a low gas pressure is that temperature will have a smaller effect on ride heights and wheel loads. At recommended pressures, change in wheel loads with temperature is not usually a big concern, but the effect is a reason not to go with extremely high pressures.

Cavitation is localized boiling of the fluid, either in the passages through the piston or on the trailing side of the piston. It causes jerky, erratic, and sometimes vibratory damping action, and is tough on the hardware as well. The gas pressure is there to prevent it.

It is hard to predict exactly when cavitation will occur, but we can say that it becomes more likely as shaft velocity increases, as temperature increases, and as damping force increases.

It is possible to design a shock to run with no gas pressure at all, or very little, but that requires the use of a foot valve or a through-shaft configuration. Actually, for a through-shaft design, it is desirable to have pressure, but the pressure doesn’t result in a shaft force.

As long as cavitation does not occur, gas pressure has little effect on damping behavior.

Because of the problem of cavitation, and because the rate of the gas spring is small and the effect of charge pressure on overall spring rate is small, I recommend adhering to manufacturer’s recommendations when choosing gas pressure for a conventional single-tube gas shock with no foot valve.

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