Torsional Rigidity. Humor me

[BradK]

I've been reading quite a bit lately, and discussing the topic of torsional rigidity. It all started when I was about to order my new car (E90 M3), and started a discussion with my friend, and owner of an E92 M3. We discussed the chassis stiffness, and I explained that the E90 body is stiffer due to the addition of a B-pillar (the body post between the front and rear door). With that added support, the car "feels" stiffer when you drive it (ie, over bumps). He got quite a laugh out of it, and thought I was a little off my rocker, thinking that I could feel such a thing when driving. I think this is especially obvious when comparing a Z3 roadster, to a Z3 coupe. "Cowl shake" was the term instantly used (courtesy of wikipedia: Scuttle shake (sometimes called cowl shake in the US) is the term used for the phenomenon experienced in many convertible or open top automobiles where, due to lower structural rigidity caused by the lack of a roof, the middle section of the chassis flexes, causing the bulkhead in front of the passenger compartment to move and vibrate when the vehicle is subject to uneven road surfaces. Passengers feel it as a noticeable vibration and shudder.) I wasn't saying that the coupe had a considerable cowl shake over the sedan, but I had to use an extreme example to make my point.

It started a discussion among him, and many co-workers here at my dealership. A lot of things were considered in this discussion on non-convertible cars; sunroofs, folding rear seats, even a ski-bag door cutout. It also made me look into the torsional specs for a Z3 coupe body. At the time that car was introduced, BMW claimed it was the stiffest chassis they have ever built. However, I was never able to find an official spec for it. Anybody ever looked into this? Also, for entertainment purposes, I found and cleanly compiled some information I found (here: http://www.germancarforum.com/test-d...-rigidity.html ), and a few other miscellaneous sites. I cannot attest to the accuracy of this information, but the data seems consistant. It's amazing how much difference there is between a coupe and convertible version of the same models. Some of these numbers are a little hard to imagine (Veyron vs Veyron Grand Sport??), but here it is:

Alfa 159 - 31,400 Nm/deg
Aston Martin DB9 Coupe - 27,000 Nm/deg
Aston Martin DB9 Convertible - 15,500 Nm/deg
Aston Martin Rapide - 28,000 Nm/deg
Aston Martin Vanquish - 28,500 Nm/deg
Audi A2 - 11,900 Nm/deg
Audi A8 - 25,000 Nm/deg
Audi R8 - (2014 MY) - 40,000 Nm/deg
Audi TT Coupe - 19,000 Nm/deg
Bentley Azure - 18,000 Nm/deg
Bugatti EB110 - 19,000 Nm/deg
Bugatti Veyron - 60,000 Nm/deg
Bugatti Veyron Grand Sport - 22,000 Nm/deg
BMW E30 M3 - 23,000 Nm/deg
BMW E36 Touring - 10,900 Nm/deg
BMW E36 Z3 - 5,600 Nm/deg
BMW E46 Sedan (w/o folding seats) - 18,000 Nm/deg
BMW E46 Sedan (w/folding seats) - 13,000 Nm/deg
BMW E46 Wagon (w/folding seats) - 14,000 Nm/deg
BMW E46 Coupe (w/folding seats) - 12,500 Nm/deg
BMW E46 Convertible - 10,500 Nm/deg
BMW E53 X5 (2004) - 23,100 Nm/deg
BMW E90 - 22,500 Nm/deg
BMW Z4 Coupe - 32,000 Nm/deg
BMW Z4 Roadster - 14,500 Nm/deg
BMW E39 5 - 24,000 Nm/deg
BMW E60 5 - 24,000 Nm/deg
BMW F10 5 - 37,500 Nm/deg
BMW F07 5GT - 31,000 Nm/deg
BMW E70 X5 - 28,000 Nm/deg
Chrysler Crossfire - 20,140 Nm/deg
Chrysler Durango - 6,800 Nm/deg
Chevrolet Cobalt - 28 Hz (conversion anyone??)
Chevrolet Corvette C5 - 9,100 Nm/deg
Chevrolet Cruze - 17,600 Nm/deg
Dodge Viper Coupe - 7,600 Nm/deg
Ferrari 360 Spider - 8,500 Nm/deg
Ferrari F50 - 34,600 Nm/deg
Ferrari 360 - 1,474 kgm/degree (bending: 1,032 kg/mm) (what does this mean?)
Ferrari 355 - 1,024 kgm/degree (bending: 727 kg/mm)
Fisker Karma - 33,000 Nm/deg
Ford Focus 3d - 19,600 Nm/deg
Ford Focus 5d - 17,900 Nm/deg
Ford GT - 27,100 Nm/deg
Ford GT40 MkI - 17,000 Nm/deg
Ford Mustang 2003 - 16,000 Nm/deg
Ford Mustang 2005 - 21,000 Nm/deg
Ford Mustang Convertible (2003) - 4,800 Nm/deg
Ford Mustang Convertible (2005) - 9,500 Nm/deg
Jaguar X-Type Sedan - 22,000 Nm/deg
Jaguar X-Type Estate - 16,319 Nm/deg
Jaguar XK - 16,000 Nm/deg
Koenigsegg Agera - 58,000 Nm/deg
Koenigsegg Agera R - 65,000 Nm/deg
Koenigsegg CC-8 - 28,100 Nm/deg
Lamborghini Aventador - 35,000 Nm/deg
Lamborghini Countach - 2,600 Nm/deg
Lambo Gallardo - 23,000 Nm/deg
Lamborghini Gallardo Super Trofeo Stradale - 35,000 Nm/deg
Lamborghini Murcielago - 20,000 Nm/deg
Land rover Freelander 2 - 28,000 Nm/deg
Lexus LF-A - 39,130 Nm/deg
Lotus Elan - 7,900 Nm/deg
Lotus Elan GRP body - 8,900 Nm/deg
Lotus Elise - 10,000 Nm/deg
Lotus Elise 111s - 11,000 Nm/deg
Lotus Esprit SE Turbo - 5,850 Nm/deg
Lotus Elise S2 Exige (2004) - 10,500 Nm/deg
Maserati QP - 18,000 Nm/deg
Mazda Rx-7 - 15,000 Nm/deg
Mazda Rx-8 - 30,000 Nm/deg
McLaren F1 - 13,500 Nm/deg
Mercedes Benz SL - With top down - 17,000 Nm/deg, with top up 21,000 Nm/deg
Mercedes Benz W212 E - 29,920 Nm/deg
Mini (2003) - 24,500 Nm/deg
Opel Astra - 12,000 Nm/deg
Pagani Zonda C12 - 25,000 Nm/deg
Pagani Zonda C12 S - 26,300 Nm/deg
Pagani Zonda F - 27,000 Nm/deg
Pagani Zonda Roadster - 18,000 Nm/deg
Porsche 959 - 12,900 Nm/deg
Porsche 911 Turbo (2000) - 13,500 Nm/deg
Porsche 911 Turbo 996 - 27,000 Nm/deg
Porsche 911 Turbo 996 Convertible - 11,600 Nm/deg
Porsche 911 (997) - 33,000 Nm/deg
Porsche Carrera GT - 26,000Nm/deg
Renault Sport Spider - 10,000 Nm/deg
Rolls-Royce Phantom - 40,500 Nm/deg
Saab 9-3 Sportcombi - 21,000 Nm/deg
Volkswagen Fox - 17,941 Nm/deg
Volkswagen Passat (2006) - 32,400 Nm/deg
Volkswagen Phaeton - 37,000 Nm/deg
Volkswagen Golf V GTI - 25,000 Nm/deg
Volvo S60 - 20,000 Nm/deg
Volvo S80 - 18,600 Nm/deg

Also, another thought was how does a hardtop bolted on a Z3 roadster change the rigidity? Does it even compare to a coupe body (comparable)? Is the "cowl shake" much improved? I have lots of questions

Oh, and by the way, I ended up ordering an E90 M3, with no sunroof, no cold weather package (no folding rear seats or ski-bag), and competition package. I love the stiff ride of my M Coupe, and wanted my M3 to be as stiff as possible. What can I say, I like it rough

[Vinci]

I seriously doubt that the hard top makes any difference at all. It isn't a structural piece and it wouldn't take much force to rip out the fasteners that mount it to the body.

[BradK]

I seriously doubt that the hard top makes any difference at all. It isn't a structural piece and it wouldn't take much force to rip out the fasteners that mount it to the body.

I would tend to agree, however I was intrigued by the figures of the Mercedes Benz SL - With top down - 17,000 Nm/deg, with top up 21,000 Nm/deg. Is there that much of a difference?

I'd like to hear from a hardtop owner and see if they "feel" any difference from the hardtop being on vs. off (cowl shake for starters)

[2000mkoop]

I've always seen it stated that the z3 M Coupe is 2.7 times stiffer than it's roadster counterpart, so if the above data is "BMW E36 Z3 - 5,600 Nm/deg", then would the coupe version be 15,120 ?

Koenigsegg Agera R - 65,000 Nm/deg........WOW

[wcampbelliv]

I feel a serious change between hardtop and ragtop. However, that could be due to worn out components. I'll let you know when I re-do my suspension if I notice such a change.

[Vinci]

I would tend to agree, however I was intrigued by the figures of the Mercedes Benz SL - With top down - 17,000 Nm/deg, with top up 21,000 Nm/deg. Is there that much of a difference?

I'd like to hear from a hardtop owner and see if they "feel" any difference from the hardtop being on vs. off (cowl shake for starters)

The SL has a retractable hard top. That's different.

[Arkangel]

NM and HZ are two different measurements, so try not to get those mixed up.

[Z-Thrizzle]

Damn the Z3 is really low. On the other hand I'm not surprised. Cowl shake and flexing is really noticeable. I have a body brace which helps but it's still far from a coupe.

[M0nK3y]

I'm once again impressed with my car. Coupes ftw

Hardtops won't do much...unless its a hardtop convertible like the new z4s

Sent using mental telepathy

[BradK]

woo hoo! Upon some further research, I found the spec!! From the BMW "Fast Facts" book (a type of training manual/reference guide for models). Quoted from the page: "At 16,400 Nm/deg, the coupe body is 2.6 times as twist-resistant as the roadster".

[JWin]

Does the relative impact of these numbers scale in anyway against the size and weight of the vehicle?

[2000mkoop]

Does the relative impact of these numbers scale in anyway against the size and weight of the vehicle?

Good question. That koenigsegg being 4x as stiff as an m coupe seems crazy!

[BradK]

I would have to "assume" it is all relative. I mean look at the Rolls Royce Phantom - 40,500 Nm/deg. I laugh every time at the Lamborghini Countach - 2,600 Nm/deg... really? What a jalopy!

[f50nut]

Ferrari F50 - 34,600 Nm/deg

And just think, that car uses the engine and gearbox as chassis parts. So the suspension bolts directly to them. F1 stuff...crazy.

[MusicCity Coupe]

Anyone else notice the calculated stiffness of a Coupe would then be only 1/2 as stiff as a Z4... Z4 FTW !!!! NOT !!!

Trust me. There is more to great handling than pure stiffness. Suspension geometry plays a big part as well, as does overall vehicle weight... and the list goes on.

[f50nut]

Trust me. There is more to great handling than pure stiffness. Suspension geometry plays a big part as well, as does overall vehicle weight... and the list goes on.

This.

Can any math experts chime in? The figures for Lotus cars on that list are comparatively low. So are those figures proportional to vehicle weight at all? Theoretically the Lotus would be under less physical stress than a much heavier car performing the same task. So that number is really only relative to the car's abilities, if it would never even reach, say, 10,000 Nm/deg during driving?

Someone let me know if I'm just making things up.

[albrazzi]

I noticed when I installed my front strut brace, not dramatic but noticeable. When I built a 4 pt rollbar tied in at the roll hoop locations mainly, there was a tremoendous benifit to stiffness What I felt as cowl shake is mostly gone, and yes I could feel it on my Z and not on any Miata I have driven.

FTIW try the last generation Ford T bird, or an older RX7 if you want to see what cowl shake really is. I would like to see the numbers on these cars.

Any one who laughs at someone who can feel it is not in tune with what he is driving. The new MB SLs retractable hardtop and all are cut from a peice of stone and stiffness is not everything but you cant do the things these designers and engineers are doing today without it.

[Gofast]

Does the relative impact of these numbers scale in anyway against the size and weight of the vehicle?

Yes, it does.
In the case of these numbers, the torsional rigidity is simply how much torque (Newton-meters) is required to deflect the plane of the front axle one degree relative to the plane of the rear axle.

This is important because a suspension can only push on the chassis as hard as the chassis can push back; once that limit is exceeded the driver will get unintended chassis deflection (scuttle shake), and therefore unintended suspension deflection which leads to less predictable handling. A more torsionally rigid chassis will be a better platform for suspension, meaning that the suspension pickups on the chassis will move less as the suspension pushes on them. This means that there will be less unintended deflection in the suspension, and the car will handle and ride better. A more rigid car can have stiffer and more tightly damped suspension while still maintaining pleasant ride quality and predictable handling.

With all that said, a heavier car will obviously "push" on its chassis harder, meaning the chassis needs to be stiffer to compensate, and a car with wider suspension pickups will tend to deflect more for a given suspension load (more leverage). This is part of the reason that race cars tend to move the suspension pickups as far inboard as possible, although that's not really feasible in passenger cars given the need for interior space.

[Arkangel]

I noticed when I installed my front strut brace, not dramatic but noticeable. When I built a 4 pt rollbar tied in at the roll hoop locations mainly, there was a tremoendous benifit to stiffness What I felt as cowl shake is mostly gone, and yes I could feel it on my Z and not on any Miata I have driven.

FTIW try the last generation Ford T bird, or an older RX7 if you want to see what cowl shake really is. I would like to see the numbers on these cars.

Any one who laughs at someone who can feel it is not in tune with what he is driving. The new MB SLs retractable hardtop and all are cut from a peice of stone and stiffness is not everything but you cant do the things these designers and engineers are doing today without it.

Pictures?

[M0nK3y]

Anyone else notice the calculated stiffness of a Coupe would then be only 1/2 as stiff as a Z4... Z4 FTW !!!! NOT !!!

Trust me. There is more to great handling than pure stiffness. Suspension geometry plays a big part as well, as does overall vehicle weight... and the list goes on.

Completely agreed. Tires, spring rates..weight and everything is a factor. But torsion rigidity is always nice to look at

Sent using mental telepathy

[BimmerBreaker]

I seriously doubt that the hard top makes any difference at all. It isn't a structural piece and it wouldn't take much force to rip out the fasteners that mount it to the body.

It doesnt have to be structural, it connects body parts and transfers the load, hardtops DO help because it forces lateral forces to be transfered across the car through the hardtop instead of just being absorbed by the car and twisting it. The fact it isnt "structural" and can be removed easily has nothing to do with the fact it serves a purpose transfering loads.

The SL has a retractable hard top. That's different.

How is that different at all? In either case it is attached to the car through some latches, really makes no difference if its a hardtop built into the car or not, in either case its not firmly attached to the frame, the ONLY difference here is whether the car installs the top, or if you install the hardtop.

Also, I find it hard to believe the Z3 is THAT soft of a frame. Maybe under 10,000N but 5600 is seriously like a mid-90s Buick... And some of those other BMW numbers are a little... off imo, X5 is nearly as rigid as the Pagani which has a carbon fiber monocoque frame?

I did a little digging, after sifting through at least 20 pages with the same identical list as you posted, I did find this:

"the M Coupé platform also boasts a significant functional advantage in terms of chassis stiffness with an unprecedented torsional stiffness of 32,000 Nm per degree, setting a new record in its segment and contributing not only to optimal handling dynamics but an exceptional level of passive safety"

Which would put the Z3 at over 10,000NM which makes a lot more sense to me. And I have heard that the Z3M coupe is STILL the most rigid BMW chassis produced, and this would go along with that. Z3 is ~12,000

And yes, theres a lot more to handling than just chassis stiffness, but a stiff chassis allows for far more predictable behaviour and can be tuned more to the limits.

[Vinci]

The Z3 hard top is not a load-bearing component. The whole top is mated to the body over soft rubber gaskets, so that it isn't damaged by body flex.

Honestly, go look at a Z3 hard top.

[Amuro Ray]

Dynamic rigidity is measured in hz, and I want to say the Z3 roadster is 18hz, MZ roadster is 18.2 an the M coupe is 29.2 (tied with the E46 3 series).


Has anyone considered making an "X brace" between the Roll bars to "connect" them? You have the roll over protection of the hoops, along with some of the benefits of a full roll bar?

[BimmerBreaker]

Amuro, we know at least one thing for fact - the M Coupe is 2.7 times stiffer than the M roadster, and I dont see how an E46 3 series is going to be more stiff than an M Coupe... also theres no difference in chassis between Z3 and Z3M...

The Z3 hard top is not a load-bearing component. The whole top is mated to the body over soft rubber gaskets, so that it isn't damaged by body flex.

Honestly, go look at a Z3 hard top.

If you are trying to tell me the entire top isnt even attached to the car, and that it just rests on top with rubber, then I question how people's tops dont come off going over bumps.

The top is attached to the car, the fact that is rubber underneath it does not in any way imply the hardtop does not help rigidity. If anything that tells us that the body would be trying to flex but instead it hits the top, thus making that rubber neccesary and the top absorbs part of that flex. The fact that the hardtop is attached firmly to the body helps it transfer small amounts of flex. Im not saying it performs like a car built with a hardtop would, but it definitely does help a small amount.

[Amuro Ray]

Amuro, we know at least one thing for fact - the M Coupe is 2.7 times stiffer than the M roadster, and I dont see how an E46 3 series is going to be more stiff than an M Coupe... also theres no difference in chassis between Z3 and Z3M...

The E46 Sedan is just as stiff as (if not stiffer)than the Z Coupe, and this isn't from me. The figures I gave you are for Hz, and measure the dynamic torsenal values of the chassis. The Z3M cars have a stronger reenforced rearsubframe, which is likely the cause of the slightly higher value.

Here you go (from Bimmer Mag 12/98):

Dynamic stiffness E46/4 29.8 hz
M coupe 29.2
E46/2 29.2
E39 29.0
E36/4 28.3
M roadster 18.4
E36 cabrio 16.6

[COLOR=blue! important]E46[/COLOR] Sedan (w/o folding seats) 18,000 Nm/deg

If you are trying to tell me the entire top isnt even attached to the car, and that it just rests on top with rubber, then I question how people's tops dont come off going over bumps.

The top is attached to the car, the fact that is rubber underneath it does not in any way imply the hardtop does not help rigidity. If anything that tells us that the body would be trying to flex but instead it hits the top, thus making that rubber neccesary and the top absorbs part of that flex. The fact that the hardtop is attached firmly to the body helps it transfer small amounts of flex. Im not saying it performs like a car built with a hardtop would, but it definitely does help a small amount.

I can't imagine that the top isn't somehow reenforced with metal, has anyone seen exactly what the top is made of? Fiberglass isn't the most flexible, something must help it keep shape.