F1technical.net

I have been pondering this for a while since the thread about tyres and heat...

A shock absorber in its simplest form is a spring and a damper; the spring is there to store energy from movement of the suspension and return the energy once the suspension is able to return to the original position. Such a process (in an ideal world) would not involve heat generation as the energy is not dissipated, only stored. However, the damper section of the shock is intended to 'damp' out vibrations and is must therefore absorb and dissipate energy. My guess is that this energy is dissipated as heat.

A logical extension of this is that the damper section of the shock absorber must therfore get pretty hot during racing conditions - BUT... the shocks are normally packed inboard of the bodywork, the front ones pretty close to the drivers feet. Does anyone have any sense of how much heat is generated, and how the dampers are cooled? Furthermore, assuming they do get hot the liquid inside the shock would presumably change in viscosity as the temperaturechanges... and therefore the damping efficieny might change... clearly this would be undesireabl, does this happen in practice?

Sure, a damper or shock absorber (SA for short) is like a resistor. In all types of SA energy is absorbed by friction forces and converted into heat. These friction forces are proportional to the velocity of friction elements.

That heat surely goes into the liquid or gas that is inside the SA, minus what it radiates. The amount of radiation, judging by the form factor most SA have, does not seem to be the main concern of the designer (no SA with cooling fins are popular, AFAIK).

F1 SA, I imagine, must generate low heat, compared with a normal damper. First, the "resistance" is limited, because the friction forces are limited, because the amplitude of movement is limited, because:

1. F1 cars have "hard" suspensions
2. F1 cars ride low

Second, the "current", or load, is smaller than in a normal car:

3. F1 cars weigh less than most cars

Anyway, let's put some rough numbers to it, following a long tradition of amateurs in this site...

The IRI (I've mentioned it before, it's the International Roughness Index) tells you how many millimeters moves up and down the body of a car when it moves through 1 meter of road. I repost the IRI model car, Mikey_s knows it better than me, I'll say only that Ms is the body, Mus is the suspension and that xs is the movement of the body:



I suppose F1 tracks have an IRI of, let's say 2 mm/m (it could be 3, maybe, but I do not want to open the calculator, so I'll round a lot from now on).

Take in account this "quarter car" used as reference has springs, weights and SA that are different from the ones an F1 car has, which means more "travel" of the body.

Anyway, let's imagine a car on a track of 5 km with 75 laps. Without calculator I round that to 400 km. The car must move up and down 800 m through the entire race (at 2 mm per meter of track).

Of course, this is the "throughtput" of energy through the resistor, not the energy damped (on the contrary, it represents the energy NOT damped, but let's assume they are of the same order of magnitude). With a gravity of 10 m/s2 I get:

Energy = m*g*h = 600 kg * 10 m/s2 * 800 m = 5 Mjoules

If the race takes 1.5 hours, which is like 5.000 seconds, give or take, you have:

Power = 5.000.000 Joules / 5.000 seconds = 1 Kwatt

This is more like 500 watts if you take in account that half of the energy (at least, if no more) goes to the rear shock absorbers.

Now, there are other things, beside SA, that adsorb energy, that is, wheels and springs, shown on the posted picture as "kt" and "ks". Let's assume that wheels and springs dissipate only half of the energy, even if that's probably conservative for an F1 car, famous for relying on wheels to provide shock absorbing power.

We arrive to a power around 250 watts, which is like three light bulbs. That's enough to keep your legs a tad warmer than my taste. Anyway, part of this heat surely can be managed by simple cooling systems.

As far as I remember, there have been posted in this site some pictures showing air vents on top of the frontal part of the cockpit, surely for cooling. I suppose the energy of the body inside a fire suit is larger than the numbers I got.

Surely I must have made some mistakes, I appreciate if somebody has the time or the interest to point them out.

Good job Ciro,

it's good that someone (in this case you) puts something up for people (including me!) to shoot at....

A couple of areas for discussion fall out from your post;

I think you are probably correct in your views of surface irregularity; I know that the tracks are (or should be - which is not always the same thing !!) at least as smooth as public highways. However, I was thinking about the damping when the cars go over the sawtooth kerbs that the energy must be much more intense than rolling over the track surface.

Next; sure the suspension is stiff, but it does move considerably; it needs to be stiff due to the large changes in downforce between static and maximum speed. The stiffness must come from the spring, then the damping is required to damp out the unwanted oscillation; therfore the energy dissipation must be capable of dissipating unwanted energy from this high stiffness system... that would suggest that quite a lot of energy must be dissipated... The cars may be quite low in mass, but at full speed they "weigh" considerably more that an road car due to the downforce.

My question was not a loaded one, I have no clue what the answer is, but it is interesting to ponder.

very good "at first sight" assumptions and calculations

I remember some here have

provided links to F1 susp test rack suppliers and such before. I imagine the information you're looking for might be fairly straightforward to derive from that kind of an information, or at least get a "ballpark" figure. Or you can contact Speed's Matchett and ask for a chalkboard session on the subject . I'm a bit pressed for time at the moment so I'll have to leave it at this for now. Interesting notions, though.

Sure, Mikey, you're right. I did not think about the aerodynamic load (as usual ). It's going to be limited to 12.500 Newton or, let's say, 1.2 tons. That'll double my numbers. You could cut them in half again if you think there are two dampers, so the numbers are valid for one damper. As I write that I think something must be wrong... I remember that figures of downforce arrive to several times the weight of the car.

On the other hand it's true that the springs are harder and thus carry more energy. I'm not sure if that means more or less load on the damper. On one side you point out that any movement of them have to imply a larger force. On the other hand they help to carry and adsorb larger forces, so I don't know. Aren't the springs analog to induction coils in a circuit? I'm not sure. Does anybody knows or have the time to search?

As you suggested in your first post, most of the work made in the springs is carried by elastic forces. I think this means they have small losses and adsorb (and emit) little energy.

Anyone has ideas? Or better yet, has anybody "seen" it in action? Next time I drive (not today, I'm afraid) I'll go under my car to feel the relative heat of springs and dampers, by touch, which is something I believe is also in the "tradition" of our posts, even if I imagine that the heat difussion and radiation from the brake pads makes any judgement of this kind useless.

Thanks, Belatti. Checkered is right, maybe modbaraban can provide better figures for total movement of body using his expertise on simulators.

I did not think about kerbs, but if I had to estimate kerbs roughness I'd put it with an IRI of 10 to 14 mm/m, which would increase the energy by a factor of 5, or maybe 7.

On the other hand this must be pondered: I doubt very much that kerbs represents over 5% of the racing length (maybe more for Räikonnen... ), so pondering this, it gives me:

Power = 0.95*500 watts + 0.05*2500 watts (over kerbs) = 600 watts

That's for two frontal dampers, taking in account the aero load. That's like having two more passengers in the cockpit. On the other hand, the cockpit is well aireated...

I think the question is nice and gives me a couple of ideas: it would be a good example when explaining gravitational energy. It also gives ballpark figures when thinking how much gas you could save with smoother roads: it's something like turning on the heater at your room or turning on a PC for each car moving on them...

The rough calculations I gave, show that, in the course of a race, is an energy enough to "elevate" the car about 1 or 2 kilometers up in the air! (or the energy that a car has after a fall of 2 kilometers. For the MythBusters fans: that's a myth I would like to see "under experimentation"... these guys let cars fall from the sky at the slightest opportunity. )

Finally, I wonder if this is an energy that could be recycled, at least in hydraulic-based energy-recovery systems. If you use Bosch electric dampers you could charge the battery and be done with the alternator... Maybe in the Prius model 2060, when oil reaches 1.000 dollars per barrel, that will be standard equipment...

[quote="Ciro Pabón"]
1) Sure, Mikey, you're right. I did not think about the aerodynamic load (as usual ). It's going to be limited to 12.500 Newton or, let's say, 1.2 tons. That'll double my numbers...
2)...Aren't the springs analog to induction coils in a circuit? I'm not sure. Does anybody knows or have the time to search?...
3)...As you suggested in your first post, most of the work made in the springs is carried by elastic forces. I think this means they have small losses and adsorb (and emit) little energy...
4)...that the heat difussion and radiation from the brake pads makes any judgement of this kind useless...
5)...I did not think about kerbs, but if I had to estimate kerbs roughness I'd put it with an IRI of 10 to 14 mm/m, which would increase the energy by a factor of 5, or maybe 7...
quote]

1) remember to use correction factor for the calculations of aerodynamic load (not the full load all the lap)
2) Damper= resistor ; Spring= capacitor ; Mass= induction coils
3) Yep
4) You bet (and the engine, too)
5) the correct form would be to integrate displacement arround a lap, this should be easy to estimate, including without a "suspension simulator"... if you play Geoff Cramond´s microprose GP4, watch out telemetry, susp displacement and measure areas below the curve (for any wheel) in your PCmonitor...

Now, there are other things, beside SA, that adsorb energy, that is, wheels and springs, shown on the posted picture as "kt" and "ks". Let's assume that wheels and springs dissipate only half of the energy, even if that's probably conservative for an F1 car, famous for relying on wheels to provide shock absorbing power.

Technically the springs do nothing to dissipate the energy, they merely store it. All the energy of the oscillating system must be damped by the dampers. Of course, the energy goes into heating the fluid in the damper as you have mentioned.

Tyres have a small damping factor, but it is very negligible and that is why the Tunable mass damper was so effective on the Renault.

Not only was downforce left out, but the inertial forces. Obviously, braking at 5g is going to put a lot more load on the front dampers. The car weighs 700kg with 50/50 weight distibution and add 12500N of aero load, neglecting cornering accelerations, just straight line braking here.

(700/4)*5*9.81 + (12500/4) = approx 12,000N of load per damper.

Assuming a very stiffly sprung car, with ride rate of approx 2.5hz, and critical damping (so that the energy is damped in one cycle)

1/2.5 = 0.4 seconds.

Easiest way to find out how much energy is damped is to find the energy stored in the spring. (I think the spring rate is pretty high, probably around 1500 lbs/in or (26775 kg/m) and using the 2mm displacement for bump.

E_k = 1/2*k*x^2 -> E_k = 1/2*(26775)*(.002)^2 -> E_k = 0.05 Joules.

Because the energy is dissipated in time, we need to find the Power

P = E/t -> P = 0.05/0.4 -> P = 0.125 Watts dissipated per 2mm bump.

Now, lets hit a kerb, 10cm displacement.

E_k = 1/2*(26775)*(.10)^2 -> E_k = 133 Joules

P = E/t -> P = 133/0.4 -> P = 333 Watts per 10cm kerb!!!



A sprung-mass damper system is governed by the following differential equation. This is a damped harmonic oscillator which follows from newtons second law.

inertial force + damping force + spring force = 0 (no forced oscillations)

which equates to (d wrt time, in terms of position x):

m*d^2(x) + c*d(x) + k*x = 0

d^2(x) + (c/m)*d(x) + (k/m)*x = 0

(c/m) = damping factor

(k/m) = spring factor

And a LRC circuit (inductor, resistor, capacitor), using Kircoff's voltage law

voltage_L + voltage_R + voltage_C = 0

which equates to (d wrt time, in terms of charge q):

L*d^2(q) + R*d(q) + (1/C)*q = 0

d^2(q) + (R/L)*d(q) + (1/LC)*q = 0

(R/L) = damping factor

(1/LC) = stored energy in capacitor

I still think this is such a weird idea that an electrical circuit and a sprung mass operate on the same principles.

Ciro Pabón wrote:Sure, Mikey, you're right. I did not think about the aerodynamic load (as usual ). It's going to be limited to 12.500 Newton or, let's say, 1.2 tons. That'll double my numbers. You could cut them in half again if you think there are two dampers, so the numbers are valid for one damper. As I write that I think something must be wrong... I remember that figures of downforce arrive to several times the weight of the car...

I don't think downforce has such a big impact in heat from dampers. It will mostly be balanced by the springs and it is to create really small and slow vertical motion. The speeds and masses to be dealt with are those from the car facing the track.

EDIT: Downforce lacks inertia for the dampers to fight, I think it's better put this way.

My 2c.

Ricardo

I found that in motorcycle racing suspension oil is changed after every race. The oil used in fork suspension should have constant viscosity, because you can get some suspension fading from heat during the race. I looked up the curves for that "marvel" oil and found this:

http://www.peterverdonedesigns.com/lowspeed.htm

Apparently, the suspension oils with a higher "Viscosity Index" are better, because they do not change viscosity so much with temperature. Even with that, viscosity is cut in half going from 40º to 100ºC for the best oils.

Ginsu, thank you very much. I think that the low energy figures you get when you put 2 mm displacement in your calculations comes from this: in 0.4 seconds, at, I don't know, 220 kph or 60 m/s, the car moves 25 m, more or less.

At 2 mm per meter, the IRI model tells that, on a smooth pavement, the total movement of the suspension of a "normal car" would be 50 mm, or 5 cm in those 0.4 seconds (25 m * 2 mm/meter). Of course, I'm again guessing in a shameless way, as the IRI model works for a car at 80 kph, a small detail that passed my atention...

The displacement of a normal car on a normal pavement at that speed is probably several times larger, but then, F1 cars have harder suspensions.

The faster you go, the larger the power you have to dissipate: you move up and down faster. At top`speeds, probably, any irregularities are felt on your fanny as hard as going over a kerb at low speed. That's why I don't understand rjsa completely: if the springs carry more weight, the dampers must work harder to restrain them from moving.

Thanks guys for the feedback on this - I am in awe of Ciro and Ginsu, maths was never my strong suit (just a simple chemist here!!).

From the link given by Ciro;

Motorcycle forks will run in the 26C (78F) temp range, rear shocks will run in the 65C (150F) range and rear reservoirs will be around 43C (110F). While motorcycle rear shocks require very high VIs (over 300) to function well over such a huge temperature range, motorcycle forks and bicycles do not. Anything over 100VI will be serviceable for them

...so they do get hot!

Like most things I guess that the real life situation is much more complex than at first sight. The dissipated energy is clearly not even close to the total energy going through the system, but it does appear to be significant and clearly the temperature increase requires a liquid with a high viscosity index to maintain stable performance as the shock heats up.

Intuitively, whilst they do heat up, the heating is not so large that they require active cooling, otherwise they would have fins on them, or even their own cooling system.
Thanks again to Ginsu and Ciro for the complex stuff!

The introduction of motorcycle shock absorber technology is interesting. Ohlin builds shocks with an external "tank" for increased capacity and as noted in the link - cooling.

http://www.motorbike-world.co.uk/frame- ... shocks.htm

Ciro Pabón wrote:That's why I don't understand rjsa completely: if the springs carry more weight, the dampers must work harder to restrain them from moving.

I'll try to express clearer, sorry, english not my language.

When you are down the straight at 300Kph and hit a bump, the wheel will push the suspension up, and that will accelerate the car body. Both spring and damper will be the link to this movement.

Downforce was compensated by the springs already, the car was travelling along a straight line, no suspension movement, no vertical speed and no damper action at all.

The point is, downforce has no inertia, so if you push a weightless wing up, the resistence will be the same as the downforce and a small amount of air resistence of the wing being pushed up, wich is nill compared to the downforce.

You are not 'accelerating' downforce, it does not count as mass and wont count into mass+damper systems. It's just a pre-load to the spring in this case.


That's how I see it, at least.

Yes, rjsa, you're right: downforce is more or less a "constant" (with an exception that I'll try to evaluate at the end). But take in account I'm trying to guess potential energy through sumatory of displacements. Many simulators and analysis software provide you with this information, as Ginsu explained.

So, when you calculate the energy based on these displacements, measured or simulated, that energy is proportional to weight. So, if you measure a displacement of 5 cm or whatever in a car that weighs 1 ton, then the energy is double if a car with 2 tons moves up and down the same amount of 5 cm, no matter if the extra ton comes from aerodynamic load or weight.

On the other hand you are right, I repeat, in the sense that if the bump and speed are the same, the heaviest vehicle will have smaller displacements. But if you calculate energy from measured displacements, then a heavier vehicle will dissipate more energy.

The exception I mentioned on the aero load being constant is this: every time the car accelerate the load increases, from, let's say 0 to 1.2 EXTRA tons. The springs are compressed. Thus, when the car brakes for the next curve, that energy stored in the springs has to be damped. I imagine this effect is small because it acts only in a small percentage of the track. If you assume it happens at every curve and it compress the suspension totally, for example 5 cm, it would add a few thousands of joules only per lap, because as rjsa explains, it doesn't vary or oscillate.

About Mickey_s being in awe, I can say this: the only subject I almost failed in highschool was chemistry. So much for exceptional abilities on my part...

Thanks, Carlos, nice link. I've never seen shock absorbers with an external tank. I wonder what's that good for.

We've had a couple of threads on shock absorbers. I think Ferrari's are exceptional: viewtopic.php?t=3886

Ciro Pabón wrote: I imagine this effect is small because it acts only in a small percentage of the track. If you assume it happens at every curve and it compress the suspension totally, for example 5 cm, it would add a few thousands of joules only per lap, because as rjsa explains, it doesn't vary or oscillate.

Hi Ciro,

It's over a short period and it is slow (1~3 sec on breaking, several seconds on accel.), i.e., easily dissipated, won't build up to heat accumulation in the damper.