Why are stiff springs more responsive?

[Adam Holland]

I know that stiff springs are more responsive than softer but why? It seems natural that this would be the case but what is happening during turn in? I read on another forum that the softer springs would store more energy than the stiff because they compress further. However two springs of different stiffness can still store the same energy according to U=.5kx^2. Others have said that the car won't turn until the body settles and stops rolling because once the body has stopped rolling [insert various explanation here]. Also it seems odd that when the tires are turned into the corner the car would be going in that direction regardless of body roll and spring stiffness even when you account for the slip angle of the tires.

So can someone explain to me in terms of conservation of energy or various equations etc. just what is happening during turn in that makes a stiffer setup respond to steering inputs quicker than a softer setup?

 

[Simon Bridge]

You need to define what you mean by "more responsive" : how would you measure "responsiveness" of a car?
... but if you imagine the extreme case of a car suspension that works by bungee chord: as the wheels turn the corner, but the car body just keeps going and going (law of inertia) many meters out past the corner until the bungee snaps it back. What would that be like to drive?
By comparison, imagine there is no suspension at all - very rough ride, but now the body follows the wheels around the corner right away.

 

[Ranger Mike]

They are not. no way ..no how! That is why racers spend a lot of time tuning and testing to get the softest spring, ARB and damper combination possible. It has nothing to do with conservation of energy.
We run soft springs for two reasons...to feel the cars response on the track ( and all tracks are rough as a corn cob)and permit the cars body minimum clearance during long straight drive time. If the car is closer to the ground vs another car, we get more aerodynamic flow and go faster than the other car.

Slip angle does not mean a thing until you understand what is going on when a car enters a left hand turn at speed.
suggest you read race car suspension class thread above and get the whole inside scoop.

 

[SteamKing]

I know that stiff springs are more responsive than softer but why? It seems natural that this would be the case but what is happening during turn in? I read on another forum that the softer springs would store more energy than the stiff because they compress further. However two springs of different stiffness can still store the same energy according to U=.5kx^2. Others have said that the car won't turn until the body settles and stops rolling because once the body has stopped rolling [insert various explanation here]. Also it seems odd that when the tires are turned into the corner the car would be going in that direction regardless of body roll and spring stiffness even when you account for the slip angle of the tires.

So can someone explain to me in terms of conservation of energy or various equations etc. just what is happening during turn in that makes a stiffer setup respond to steering inputs quicker than a softer setup?

It's not a matter of spring energy, at least not chiefly.

For non-race track applications, springs with higher rates are usually chosen because they tend to keep the tires on the road better in turns and on rough driving surfaces, and the better contact which is maintained between tire and road surface usually translates into better handling, especially in turns. A good set of shock absorbers (dampers) helps this, because they will quickly damp out spring oscillations due to striking bumps and thus keep the tires in better contact with the road.

Suspension tuning has always been one part science, one part engineering, and one part art. You can buy textbooks which tell you how to calculate certain responses that different automotive suspension components will give, but even with advances in computers and whatnot, designers still use a lot of real-world testing of vehicles to determine the best combination of spring rates, tires, shocks, roll bars, etc. to give the best-handling vehicles without sacrificing (too much) ride comfort.

Active suspension technology can use computers in the car to adjust itself to different road surfaces and driving conditions.

 

[Ranger Mike]

the original post was asking about responsive.
now granted..two exact same vehicles of same weight, same engine size, gearing etc.
the only difference being the spring rates..
stiffer springs can make for better handling in some cases ( vehicle set up was not set up for optimal handling). This is the stock grocery getter with spongy springs that washed out in that first fast turn due to spring rate overload.
"stiffer springs" are more " responsive" compared to stock springs, in the sense that they can handle the momentum of the vehicle in a turn with " better" than the stock spongy spring set up. You are driving in the same turn with the same speed, same tires, same weight and same momentum. The stiffer spring keeps the front end from washing out ( understeer) better than the soft springs that pancake..IN MOST CASES. If you go too stiff on spring rate you get no suspension travel and you push due to no trie adhesion. You are scrubbing the tire contact patch.

In some cases the stiffer spring will dramatically impair handling. (vehicle was set up at optimum but the stiffer springs took away that handling advantage).
corvette set up for max handling but we bumped up the front spring rate too much...snow plow to the track guard rail...uggg
this is why racing set up and handling is not learned fast. I have to take exception to steam king..all of these variables can be measured. Measurement is the language of Science. Engineering is a hands on practical part of Science. The art form stuff comes from a lot of mind games the race teams use on each other as a competitive strategy.

 

[Adam Holland]

By responsiveness I mean how quickly the car changes direction. Say going through the eases at COTA. I'm reading through the other forum on suspensions also so maybe I'll find the answer I'm looking for there. But I'm specifically looking for WHY in scientific terms a stiffer spring rate is typically quicker to react to steering input if that makes sense.

 

[SteamKing]

By responsiveness I mean how quickly the car changes direction. Say going through the eases at COTA. I'm reading through the other forum on suspensions also so maybe I'll find the answer I'm looking for there. But I'm specifically looking for WHY in scientific terms a stiffer spring rate is typically quicker to react to steering input if that makes sense.

Response to steering input is largely determined by the type of steering mechanism (rake & pinion, recirculating ball, etc.) and what is known as the turning ratio of the steering wheel, lock-to-lock. A quick steering car will have a low ratio for turns L-L to give greater movement to the front wheels. Spring rates don't normally affect this, AFAIK.

 

[Ranger Mike]

Stiffer springs reduce the distance of suspension travel caused by momentum while corner. The name of the game is minimal camber change...goes back to tire contact patch. And in racing ..it is all about tire, Tires, TIRES.

Increase the spring rate and you increase tire heat generation, but you will increase responsiveness to the driver. You are making the suspension more like a Go Kart which is the ultimate steering input / response situation. When you go too big on the spring rate the set up is so stiff you go into bump steer on the track where tire lose grip bouncing over the asphalt strips used to repair cracks in the pavement. We ran into this at Indy, and m y driver almost lost a filing in his tooth because the track was so rough.The good side is that the drive correction time is better. The down side is reduced grip on the suspension geometry of a performance setup. (with no other changes made after swapping in the heavier springs) . This stiffer spring set up will increase grip on a poorly designed suspension system ( stock grocery getter). Mechanically when you turn a typical front end suspension the spindle caster jacks up one side of the suspension due to caster design and king pin inclination angle. Since the spring is being compressed by the car body and turning momentum when this is going on , the stiffer spring translates the steering input through the linkage , spindle and tire contact patch to the pavement quicker than the mushy softer spring does. So you have quicker response THAN THE STOCK SPRING.
And this is probably what you are asking..I think..with no other changes, on a poorly designed stock suspension, adding spring rate only, will increase your steering feedback and add more grip than you had before the swap.
hope this helps and keep reading the race car suspension class stuff..its all in there..

 

[jack action]

The first goal of a suspension is to absorb the vertical shocks caused by the road. In that matter, any vibration analysis will tell you that the softer the suspension, the better the wheel will follow the road without altering the body motion (Only the wheel moves, not the car). Since you need the tire to be in contact with the ground for it to perform, hence the softer the suspension, the better the suspension. A practical limit is generally imposed by suspension travel, which increases with a softer suspension.

HOWEVER...

Performance-wise, it is all about maintaining the highest level of grip for the tires. The average friction force you can get from a set of identical tires is when the weight they support is spread equally between them. This means 25%-25%-25%-25% will always be better than, say, 30%-35%-20%-15%.

Going into a curve, weight transfer is inevitable, i.e. more weight on the outside wheels, less on the inside ones. The goal is thus to limit the weight transfer as much as possible. As you enter a curve, the weight transfer begins ... and stops when equilibrium is reached. With no suspension (i.e. the stiffest set-up), it means going from zero to maximum weight transfer. With a soft suspension - because of the inertia of the car body that started rolling - you will have at least one overshoot before settling in. Physically, an overshoot means the spring was compressed more, so the dynamic weight transfer is temporarily larger than the expected «stabilized» weight transfer. This reduces the overall grip of your tires and it means sliding (friction loss) can begin at a lower speed than expected.

Furthermore, the suspension geometry is designed to position the tires to perform at their best. A soft suspension means suspension travel which mean altered suspension geometry. You can designed your suspension geometry for the expected «stabilized» wheel-to-body position into a curve at a the desired speed ... and then you hit a bump and all your nice design is lost! In this case, a stiff suspension means little to no motion, hence predictable suspension geometry.

So - in summary - the softer, the better. Especially for a bumpy road, especially in a straight line (even then, relying on aerodynamics, variation of ride height can be an important factor). When in a curve, softer is still better, but not as to create too much change in the suspension geometry or to momentarily increase too much the weight transfer.

The perfect balance will always depend on the track you ride, hence why racers need adjustable suspension to always be at their best.

 

[Ranger Mike]

.

Jack Action as usual has given the correct answer and I do not want to nit pick as it is quite comprehensive.
And regarding a point of view from a Design point..he nails it.
From a race car point of view..close.
Racers do not do things from any standpoint other than winning and to win it is all about tires. Specifically, tire contact patch is the whole ball game. What ever you can do to maintain the optimum tire patch is important. From a physics point of view when cornering, we have to deal with load transfer. When cornering if we were to put the race car on a set of scales, the front end would act like it had more weight on it than when at rest. This is a simple way to explain “ weight transfer”. What really is happening is momentum from a car at speed continues in a straight line path until acted upon by an outside force. In this case, it is the race track ( immovable ) interacting wit the tire contact patch. The tire contact patch is the meeting point where the cars momentum will be scrubbed off as the tire surface shears, ( is in an under steer conditions or is “ pushing”) or the momentum is diminished by tires gripping ( but not shearing thus converting momentum to friction) and the spring / damper compressing ( converting momentum to heat as springs and dampers compress).
However...
It must be understood that a tire will have more holding power or grip if it has a certain amount of down force.
Take a tire / wheel inflated to proper pressure and stand it up like it is mounted on your vehicle. Try to slid it on the concrete garage floor. Pretty easy , right?
Now have the neighbors fat kid sit on the tire. try to slide it. You will find it’s a much tougher effort. Fat Albert has imparted download on the tire increasing its grip.

We need down force to help stick the tire that is handling the turn or corning load. We want to use the load transfer in a good way to stick the tire and the balance of the transferred load (force) will be dealt with using the proper spring rate, ARB, ( anti roll bar ..sway bar). Damper or shock controls the rate of compression of this combination. If we have too much down force we go into tire shear as the tire contact patch is overwhelmed. We get down force by body roll, and sometimes aerodynamic down force.
The take away is we need to deal wit the momentum to our best advantage.
hope this helps a little.

 

[gjonesy]

So can someone explain to me in terms of conservation of energy

The shortest simple answer is energy transfer rate. Stiff springs offers more resistance to rebound under a load. The energy wave or motion moves faster through it. Where as a soft spring doesn't its slower to respond so has less resistance to energy stored, the energy wave or motion moves through the soft spring slower.

Eample

https://www.google.com/url?sa=t&source=web&rct=j&url=intent://www.youtube.com/watch?v=eCMmmEEyOO0#Intent;scheme=http;package=com.google.android.youtube;S.browser_fallback_url=http%3A%2F%2Fm.youtube.com%2Fwatch%3Fv%3DeCMmmEEyOO0;S.android.intent.extra.REFERRER_NAME=https%3A%2F%2Fwww.google.com;end&ved=0ahUKEwjjvLuAiOLKAhUDSiYKHbNmC6wQjjgIJTAC&usg=AFQjCNGZdIsaID_E8H7vGxVJK5A7pHFLiQ&sig2=iW1B0PgBjvR22mOj0jLkzg

 

[Adam Holland]

Just had that lightbulb moment. What Ranger Mike was saying very good and insightful and got me thinking in new ways. But it was just missing the bits I needed for the answer I was looking for but I didn't know how to explain it what I was looking for. What ever it was though Jack Action had it. So a big thanks to both of you as your comments together were exactly what I needed. Still making my way though the design class thread. Pretty mind numbing and confusing at times but still great. Thanks again.

 

[Adam Holland]

Actually Ranger Mike I do have one more question that's been really bugging me. When talking about calculating required spring rate in your suspension class, I think on page one or two you gave a formula to find the G-force in a corner:

G = 1.225 x R / T squared
R= Radius of the turn in feet
T = Time in seconds to complete a 360 degree turn

I'm an engineering student hoping to get into the wonderful world of racing and I have to know...how did you get this formula?

If I'm reading it correctly then G is the g-force, or as the equation would output, the fraction of acceleration due to gravity on Earth. ei: .9 would be 90% of acceleration due to gravity. R is the radius of the circle, and T is the period. After digging out my physics 1 notes I did some clever algebra and got that G=1.225v^2/r which makes sense as this is the equation for centripetal acceleration.

The part that bothers me is your constant, 1.225. I can't seem to figure out where that came from. If my assumptions that G is basically a ratio of your centripetal acceleration over the acceleration due to gravity (a_c/g=G) then you divide by 32.2 in standard units ( ft/s^2) and the G is unit less. However clearly 1/32.2 isn't 1.225.

Do you think you could clarify?

 

[jack action]

The part that bothers me is your constant, 1.225. I can't seem to figure out where that came from. If my assumptions that G is basically a ratio of your centripetal acceleration over the acceleration due to gravity (a_c/g=G) then you divide by 32.2 in standard units ( ft/s^2) and the G is unit less. However clearly 1/32.2 isn't 1.225.

The circumference of circle ...
G= \frac{a}{g}= \frac{v^2}{gR}= \frac{\left(\frac{L}{T}\right)^2}{gR}= \frac{\left(\frac{2\pi R}{T}\right)^2}{gR} = \frac{4\pi^2R}{gT^2} =\frac{4(3.14)^2}{32.2}\frac{R}{T^2}= 1.225\frac{R}{T^2}

 

[Randy Beikmann]

To the original question, the "responsiveness" of the car (how quickly it responds to steering inputs) depends on how quickly the car reacts to load transfer, to where the tire forces stabilize at their new steady value. As you steer into a left hand curve, the lateral tire forces cause lateral acceleration to the left, and load transfers from the left tires to the right tires. This means the right springs compress, and the left springs stretch. The car rolls (leans) to the right.

But of course the car doesn't roll to its new angle instantly. How quickly it settles in depends on how far it needs to roll, and its natural frequency in roll. Stiffening the springs reduces the necessary roll angle, and increasing the natural frequency increases how quickly it can roll. The result is that the car gets to its new "equilibrium" attitude more quickly. (Cars with soft springs tend to "wallow around".)

My son has a Pontiac Solstice that started off with a base suspension, and we changed it to the Z0K springs and anti-roll bar package. Everything was about 80% stiffer. The quickness of response was amazing. It felt like there was no delay or roll, and that the car was being pushed into the curve by a force applied at the CG height. After a few weeks we got used to it, and we could feel the (slight) lag.

Note that responsiveness is a separate issue from ultimate cornering g's (which pretty much depends on the tires) or road holding (which is how well the suspension keeps the tires steadily contacting the pavement over bumps). Often softer springs and proper damping will increase traction, but stiffer springs will quicken response.

 

[gjonesy]

To the original question, the "responsiveness" of the car (how quickly it responds to steering inputs) depends on how quickly the car reacts to load transfer, to where the tire forces stabilize at their new steady value. As you steer into a left hand curve, the lateral tire forces cause lateral acceleration to the left, and load transfers from the left tires to the right tires. This means the right springs compress, and the left springs stretch. The car rolls (leans) to the right.

But of course the car doesn't roll to its new angle instantly. How quickly it settles in depends on how far it needs to roll, and its natural frequency in roll. Stiffening the springs reduces the necessary roll angle, and increasing the natural frequency increases how quickly it can roll. The result is that the car gets to its new "equilibrium" attitude more quickly. (Cars with soft springs tend to "wallow around".)

Motion (energy) transfer speed, is what it all boils down to.

 

[Ranger Mike]

I was on another post on Mechanical Engineering talking about why stiffer springs are more responsive. First of all, Responsive is a pretty much arbitrary thing as you can not hang a number on it. Let us focus on a standard grocery getter commuter car with suspension designed for everyone from Grandmother to the hog dog teenager. When we drive into a left hand turn, forward momentum will cause the car to roll to the right as stationary asphalt causes the tire contact patch to push back on the momentum force. Since we have soft springs which compress under this load we have a steering feed backs that feels like mush.

The trick here is to think in 4-D. In a turn we are dealing with X,Y,Z movement and Time. Things are not 2-D as typically indicated in many discussions on this matter.
The front suspension on todays automobile have spindles that turns via the steering wheel ( thru linkage to the steering box or Rack and Pinion mechanism). These spindles are mounted in such a way that they have caster. Like a fork on a bicycle the top of the front wheel fork is slanted toward the rear and the bottom of the fork is slanted forward. Anyone who ever road e bike knows this arrangement cause self centering which adds to the stability of the steering. Same with the spindle on a race car. The spindle is slanted so the top is slightly behind the axel center line and the bottom is slightly forward of the axel center line. This Caster causes the race car to lift slightly when the steering is turned because the whole arc of rotation is tilted to begin with. Add to this dynamic , the fact that the spindle is made with an inclination angle between 5 and 10 degrees. When the spindle is turned the part that mounts the tire and wheel actually lifts the chassis. The combination of caster and Spindle inclination angle (SIA) can lift the right front of the race car and inch when turning the steering wheel.

By feel, adding a stiffer Anti Roll Bar (ARB) or sway bar ,we keep the car from rolling over like a big old whale in the turn ( stiffer front springs will do the same). With less spring compression to deal with the forward momentum, the tires must take up more of the load being transferred. In most cases they do not and we have a classic under steer condition. Race car Pushes like a freight train. Stiffer springs make the car lift on that corner a lot quicker than the softer springs trying to cope with the load coming forward and then pushing up on that corner of the car due to Caster and KIA. So the steering on stiffer springs / ARB is more “ responsive”.

So what is the answer? Just like in life, balance is the key. A good spring package and sway bar set up and good shocks to time the compression and rebound is the ticket.

 

[Randy Beikmann]

You actually can measure responsiveness. It's done by driving straight ahead at a certain speed, quickly steering by some steering wheel angle (basically a step input), and measuring the car's lateral acceleration and yaw rotation rate. (This takes a very large flat paved area to do, since different cars take on different arcs.) From this you can calculate the car's transfer function from steering to cornering. Of course the quicker the acceleration and yaw rates ramp up, the more responsive you'd say it is.

Good references for this are Gillespie's "Fundamentals of Vehicle Dynamics," Wong's "Theory of Ground Vehicles," and Milliken's "Race Car Vehicle Dynamics."

No matter what springs or tires a given car has, the final load transfer is the same, at a given lateral acceleration. But the stiffer the springs and anti-roll bars, and the higher the tires' cornering stiffness, the quicker it will reach it.

 

[Ranger Mike]

good information..guess my library will get updated with these books..thank you...

 

[akashram]

A stiffer set up distributes the cars cornering loads much more evenly than a softer set-up that will store up more kenetic energy in the outer springs/dampers. To keep it simple, body-roll puts more weight on the outside tyres of the car, which means two of your tyres are doing most of the work whilst the inner two do very little.Anti-roll bars stop one side of the cars suspension from doing all the work by connecting the left and right-hand suspension arms to each other and to the chassis, which gives 'stiffness' without hampering 'suppleness' like stiffer springs/dampers would.

 

[Randy Beikmann]

A stiffer set up distributes the cars cornering loads much more evenly than a softer set-up that will store up more kenetic energy in the outer springs/dampers.

Actually, stiffer springs increase the variation in tire loads. Because F = kx, a given deflection of one spring will produce more change in force. Also, as the car goes over a slowly undulating surface, some tires move up and others down, and these deflections result in larger force variations than if it has softer springs. (Over shorter bumps, it gets more complicated, as the tire itself "hops." Traction varies with each bump, and the car becomes "skittery.") Cars with stiffer springs also require more attention to their initial spring deflection when sitting on a level surface, needing shims to keep loads equal side to side.

To keep it simple, body-roll puts more weight on the outside tyres of the car, which means two of your tyres are doing most of the work whilst the inner two do very little.

This is true, and the total load transfer to the outside tires is the same regardless of the springs, shocks, or anti-roll bars.

Anti-roll bars stop one side of the cars suspension from doing all the work by connecting the left and right-hand suspension arms to each other and to the chassis, which gives 'stiffness' without hampering 'suppleness' like stiffer springs/dampers would.

Anti-roll bars change how much of the total load transfer each axle will produce. If you have equal spring rates front and rear, and you transfer a total of 800 pounds from left to right side, both front and rear axles would see 400 pounds of load transfer. By putting on a front anti-roll bar, the front roll stiffness becomes higher, and the front axle might see 500 pound transfer, while the rear would see 300 pounds. The car will also lean a bit less. You could also install an even stiffer front bar, and add a rear bar, to keep the same 500/300 pound transfer, while reducing roll (and increasing responsiveness). In either anti-roll bar setup, the load on the front tires becomes more unequal than the rears, which reduces their total cornering stiffness and creating understeer.

I wouldn't say that suppleness is preserved with stiffer anti-roll bars. The effective spring rate is still increased by stiffly tying left to right tires, resisting vertical motion of each.

As one of my driving instructors put it, a car with stiffer springs (and anti-roll bars) will respond quicker, while softer springs will give you better traction (given the right damping). I thought that was a very good "layman's terms" explanation that was still physically correct.

Besides the above references, my book (mentioned below) also covers the basics of this.

 

[Randy Beikmann]

Springs and Anti Roll Bars (swaybars) do not store energy. They convert momentum to heat energy. Shock absorbers (dampers) do this as well but primarily control the timing of the compression and rebound action. Just trying to encourage proper terminology , folks!

Springs and anti-roll bars are both made of steel, which is an elastic material. They do indeed store potential energy according to E = (1/2)*k*x^2. That's why a car with bad shocks will bounce seemingly forever. In vibration, a spring force is generally referred to as a "restoring force" because the energy used to deflect it is restored as mechanical energy to the rest of the system as it rebounds.

Dampers, on the other hand, are there to dissipate mechanical energy as heat. That keeps your car from building up a bouncing motion that would be uncontrollable. Proper damping is crucial to road-holding (keeping the tire in relative even contact with the road), and to prevent excessive and oscillating roll when turning into a corner.

 

[Ranger Mike]

boy did i make a mistake...forgot about Pe and Ke...good catch Randy...

 

[Randy Beikmann]

boy did i make a mistake...forgot about Pe and Ke...good catch Randy...

We all do it, don't we? Let me know when I do!