19 replies to this topic

[SteveCanyon]

I was thinking earlier about cars that have little suspension travel and how they rely on tyre spring rates to be a big part of the suspension picture.
Now I'm the first to admit it's probably a daft idea but instead of filling the tyre with just a regular gas, how would a semi-solid (along the lines of an aerogel) go to damp the motion of the tyre and so provide some kind of effect similar to that of a damper on regular suspension? Would there be any point? I've certainly seen the big baggy tyres used on some drag cars flap around horrendously and thought that since they can't use more pressure nor thicker rubber they might benefit from some way of controlling the thin rubber some other way.

[gruntguru]

I was thinking earlier about cars that have little suspension travel and how they rely on tyre spring rates to be a big part of the suspension picture.
Now I'm the first to admit it's probably a daft idea but instead of filling the tyre with just a regular gas, how would a semi-solid (along the lines of an aerogel) go to damp the motion of the tyre and so provide some kind of effect similar to that of a damper on regular suspension? Would there be any point? I've certainly seen the big baggy tyres used on some drag cars flap around horrendously and thought that since they can't use more pressure nor thicker rubber they might benefit from some way of controlling the thin rubber some other way.

Must admit to similar thoughts on many occasions. Biggest problem is unsprung mass, especially when you consider the tyre as a spring - then in that system the tread is the unsprung mass - very light.

[Tony Matthews]

I've certainly seen the big baggy tyres used on some drag cars flap around horrendously and thought that since they can't use more pressure nor thicker rubber they might benefit from some way of controlling the thin rubber some other way.

I thought that the super-flexible sidewall was deliberate, and a way of changing the effective gearing, the overall diameter of the tyres changes enormously with revs. Or am I wrong again...? On reflection, I think I might be!

[cheapracer]

I thought that the super-flexible sidewall was deliberate, and a way of changing the effective gearing, the overall diameter of the tyres changes enormously with revs. Or am I wrong again...? On reflection, I think I might be!

No you are correct, tyre growth on drag cars is a gearbox in itself.

[gruntguru]

Yes, an infinitely variable transmission at that! The super flexy, very low pressure tyres have other benefits. First, a huge (static) contact patch to distribute the drive load over a large area of the very soft tread. Second, a very "softly sprung", low mass contact patch to soak up any vertical disturbance of the track surface or the car with minimal variation in normal force. Third, when the rear of the car is jacked up by the growing tyres, the vertical acceleration is reacted at the contact patch - significantly increasing traction at the most critical point of the drag race, t=0

The downside is "tyre shake" - uncontrolled oscillation primarily of the vertical spring formed by the tyre and the mass of the car. Any experts out there that can elaborate on tyres shake? I would be fascinated to learn. I think this is the most obvious application for Steve (Bill's) suggestion. If someone came up with an ultra light closed-cell (or semi closed) damping foam to fill the tyre, it could eliminate tyre shake.

[DaveW]

A few problems spring to mind immediately.

Dissipating energy results in heat &, since tyres are good thermal insulators, a mechanism would be required to channel the heat to the wheels, etc.

Damped tyres would not react quickly to changes in load. The implications of that are legion, I think. Relaxation length, reacting to road inputs, NVH, etc., etc.

I'm sure there are others.

[SteveCanyon]

The downside is "tyre shake" - uncontrolled oscillation primarily of the vertical spring formed by the tyre and the mass of the car. Any experts out there that can elaborate on tyres shake? I would be fascinated to learn. I think this is the most obvious application for Steve (Bill's) suggestion. If someone came up with an ultra light closed-cell (or semi closed) damping foam to fill the tyre, it could eliminate tyre shake.

Exacery - I only picked aerogel because I'm not well-versed in such materials and that seemed likely to be close to what's needed. Aerogel is extremely light, it would add only a minute amount of mass to the wheel assembly.
I still wonder if effective tyre spring rates on circuit cars would benefit from this at all? Again it's just a random brain-fart ....

[gruntguru]

Exacery - I only picked aerogel because I'm not well-versed in such materials and that seemed likely to be close to what's needed. Aerogel is extremely light, it would add only a minute amount of mass to the wheel assembly.
I still wonder if effective tyre spring rates on circuit cars would benefit from this at all? Again it's just a random brain-fart ....

Thank goodness! Precisely targeted brain-farts scare the hell out of me.

[gruntguru]

Dissipating energy results in heat &, since tyres are good thermal insulators, a mechanism would be required to channel the heat to the wheels, etc.

For the dragster case, wouldn't the damping energy required be less than the catastrophic energy generated by tyre shake?

Damped tyres would not react quickly to changes in load. The implications of that are legion, I think. Relaxation length, reacting to road inputs, NVH, etc., etc.

I hear you. Even "wheel balance" would become a problem if tread deformations persisted too long after rotating away from the contact patch.

Dave, what is a typical damping ratio for tyres? (loaded question, I guess it depends which mass you are considering) I assume they are highly underdamped WRT the vehicle unsprung mass? What if the damping ratio remained substantially less than one even with the additional damping? I suppose the damping ratio for the "tread mass/tyre vertical spring" system is already 1.0 or higher and we can't afford to increase it?

[DaveW]

what is a typical damping ratio for tyres?

A piece of string springs to mind (apologies). For two examples, a high end rear drive road sports car on treads & an F1 vehicle on slicks, both tested at ambient, the phase angles of the "gross" tyre stiffness @ 7Hz were between 3 & 7 degrees.

For the record, vertical stiffness = gross stiffness * cos(phase angle), equivalent viscous damping coefficient = gross stiffness * sin(phase angle)/(2 * pi * 7) in force/unit velocity units. I hope that makes sense.

The ratio of sportscar/F1 vertical tyre stiffness was almost 2....

[J. Edlund]

Foam filled tires have been commonly used in rallying.

[DaveW]

Foam filled tires have been commonly used in rallying.

Phase angles for Pirelli rally tyres (similar conditions) averaged 11 degrees. Stiffness ratio Pirelli/F1 was almost 3.....

[munks]

A piece of string springs to mind (apologies). For two examples, a high end rear drive road sports car on treads & an F1 vehicle on slicks, both tested at ambient, the phase angles of the "gross" tyre stiffness @ 7Hz were between 3 & 7 degrees.

For the record, vertical stiffness = gross stiffness * cos(phase angle), equivalent viscous damping coefficient = gross stiffness * sin(phase angle)/(2 * pi * 7) in force/unit velocity units. I hope that makes sense.

Sorry, I'm not quite following. I may be a bit slow with regards to Fourier transforms and the like (and if I'm hopeless, so be it ...). Would the phase angle of a tire represent the amount of rotation for a deformation to make a full cycle (for the given load)? Or could you provide me a more apt physical description of a tire's phase angle?

... And in the damping equation, is that 7 in the denominator from the frequency or degrees?

Edited by munks, 26 July 2010 - 18:21.

[DaveW]

Sorry, I'm not quite following.

Apologies.

The frequency response function of contact patch load per unit deflection is complex (has real & imaginary components), in general, & can be said to have a "magnitude" (or gross stiffness) and a "phase angle" at a nominated frequency. A response function of a pure spring would have a constant magnitude (the spring stiffness) and zero phase angle (indicates no loss in energy). At the other extreme, the response function of a pure viscous damper would have a magnitude that increased with frequency and a phase angle of 90 degrees. Choose a frequency (f), read the magnitude (M), and the damping coefficient is defined as M/(2 * pi * f), since sine (90 dgrees) is unity - see previous post.

A tyre will have a stiffness & it will also dissipate some energy. The "gross" stiffness and the "phase angle", extracted from a tyre load/displacement response function at a chosen frequency, is a simple way of describing both stiffness & damping coefficient, using the relationships defined in my previous post. (Incidentally, the numeral 7 you queried referred to the frequency (Hz) at which the numbers were extracted.)

For completeness (i.e. please ignore this for now), I should add that tyre damping is a mixture of viscous & hysteretic, & all properties vary with just about anything you care to mention.

I hope that this helps.

[gruntguru]

I hope that this helps.

Helps clarify what a muddy issue this is.

[Lee Nicolle]

Race tyres have so many variations in construction, constrution material etc. Drag tyres [top echolon cars] are high growth comparitivly stiff tyres. Bracket cars are closer to a road tyre though soft compound and light construction but do not grow much.Dirt speedway tyres vary greatly. Compare a Hoosier with an American Racer no comparison. The Hoosier is stiffer, heavier then the AM but in the end work similar. Virtually all are wrinkle wall making a longer contact patch under accelaration. Both make high growth tyres, most left rears are though you can also get a belted tyre that doesnt grow much. Lower divisions use tyres that have some vague similarity to a road tyre as do a Sprintcar and sedan steers.. Though are 1 or 2 ply bias belted.Average pressure is rear about 6lb- 10 lb, steer 12-16 lb
Road race tyres can be wildly different too.Some are steel belted, some are Kevlar belted, some still are bias belted, some have soft walls and some have very stiff hard walls. That suit the same cars! Some springing and shock changes are required for different brands and construction and the stiff case tyres tend to be heavier. And ofcourse growth is either zero or very small. The Sports Sedan Dunlop rear is a wrinkle wall tyres which can really hook you up out of slow corners. I think there are others too of similar construction
Most road race tyres tend to like around 28 -35 lb hot

[DaveW]

Helps clarify what a muddy issue this is.

OK... Try this.

If the upright, wheel & tyre is removed from the vehicle & arranged (& constrained) so that the tyre supports the assembly & the upright can move only vertically, then (roughly) tan(theta) = 2 * zeta, where theta is the phase angle of the tyre frequency response function extracted at the natural frequency of the assembly. Zeta is the damping ratio of the assembly.

Hence, from my example, if the phase angle is 7 degrees (& the natural frequency was 7 Hz), then the damping ratio of the assembly would be tan(7 degrees)/2 = 0.061, or 6.1 percent of critical....

The significance of my choice of 7 Hz is that it is close to the natural frequency of the heave mode of an F1 vehicle with a locked suspension.... The reality is a little more complicated because, whilst the front axle of an F1 vehicle is effectively locked, the rear isn't - so the rear dampers dissipate most of any disturbance energy (usually over 80%). The implications are that an F1 vehicle relies on D/F to keep its wheels on the road, & the rear load variation is higher than it might be. The result is a) rear tyres tend to over-heat b) poor traction out of low speed corners & c) significantly reduced grip when following another vehicle (particularly so at the front axle).

[gruntguru]

If the upright, wheel & tyre is removed from the vehicle & arranged (& constrained) so that the tyre supports the assembly & the upright can move only vertically, then (roughly) tan(theta) = 2 * zeta, where theta is the phase angle of the tyre frequency response function extracted at the natural frequency of the assembly. Zeta is the damping ratio of the assembly.

Hence, from my example, if the phase angle is 7 degrees (& the natural frequency was 7 Hz), then the damping ratio of the assembly would be tan(7 degrees)/2 = 0.061, or 6.1 percent of critical....

The significance of my choice of 7 Hz is that it is close to the natural frequency of the heave mode of an F1 vehicle with a locked suspension....

If the front suspension is effectively locked, is the response of the "wheel+upright<>tyre" system all that relevent?

Edited by gruntguru, 27 July 2010 - 09:39.

[DaveW]

If the front suspension is effectively locked, is the response of the "wheel+upright<>tyre" system all that relevent?

Ouch. I was merely trying to be strictly accurate (pedantic) whilst trying to demonstrate how gross stiffness phase angle can be interpreted.

[gruntguru]

Ouch. I was merely trying to be strictly accurate (pedantic) whilst trying to demonstrate how gross stiffness phase angle can be interpreted.

Sorry. Not trying to be critical - I just don't have a good enough understanding of this theory to recognise your motive.