Speed estimate from rim deformation?

[gerhardf]

Hello,

can anybody please point me to something that would help me estimate a minimum impact speed that would have been necessary to cause the deformation of a (steel) rim? It's pretty badly hurt...

Thanks,
Gerhard

 

[GregLocock]

If the wheel hits the kerb square on then it is possible to estimate the force involved at a given speed, to within about a factor of two.

To relate that force to a level of damage on the rim is rather more difficult.

The simplest cheapest and most accurate method would be to repeat the accident at different speeds.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[gerhardf]

Thanks, Greg... I guess that would be the most accurate method, but I'm not sure it would be the cheapest

I guess what I was hoping for is a collection of pictures of damaged rims with a brief description of how it happened and at what speed -- just to give me an idea of what might be involved in causing a given damage.

 

[GregLocock]

That sounds like useful information for an accident investigation. Perhaps you could speak to one of them, or the cops.

Roughly speaking if I were to waste my time trying to calculate this it would cost you at least 24000 dollars, and would really need the test doing anyway for correlation!



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[CapriRacer]

Gerhardf,

You've got an almost insurmountable problem as the first thing that is hit is the tire and the inflation pressure is going to greatly affect how much the eneragy is absorbed BEFORE the object deforms the rim!

So unless you absolutely know the pressure, I don't think you can make a reasonable estimate on the speed.

 

[GregLocock]

"the inflation pressure is going to greatly affect how much the eneragy is absorbed"

No it doesn't.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[patprimmer]

I expect the inflation pressure is going to influence the extent of the deflection in the tyre, and as a consequence will effect the speed of impact required so the tyre deflects enough to allow rim damage from impact between rim and kerb.

I also expect that the angle of impact, height of kerb, shape of kerb (in particular top edge angle and radius) spring rate, shock rate, carried through dynamic effects from speed change and road surface profile shortly before contact will all have an influence. For instance if the suspension is at full droop or full compression instantly before impact will have an influence. Even the temperature of the oil in the shocks will have some influence.

All in all, a complex calculation, based at best on dubious input data.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[crysta1c1ear]

I took a stab at this for myself, just to see what sort of speeds we might be talking about, and to get an idea what might be going on. The physics here might be very dodgy, but I didn't want to just say "too many variables, very complicated", and leave it at that.

      REM Written in BBC BASIC - will run on free demo version from here:-
      REM [URL unfurl="true"]http://www.cix.co.uk/~rrussell/products/bbcwin/bbcwdemo.exe[/URL]
      *FLOAT 64 : REM Precision for real number arithmetic
      
      REM Define Units
      REM ------------
      
      percent=1/100
      
      kg=1 : m=1 : s=1
      mm=m/1000 : cm = m/100 : km = 1000*m
      cm2 = cm*cm : m2 = m*m
      
      minute=60*s : hour=60*minute : day=24*hour
      inch=2.54*cm : foot=12*inch : yard=3*foot : chain=22*yard : furlong=10*chain : mile=8*furlong
      
      mph = mile/hour
      kmh = km/hour
      
      N=kg*m/s/s : Pascal=N/m2
      atm=101325*Pascal
      
      radius = 1
      diameter=2*radius

      REM Assumptions
      REM -----------
      
      kerb_height= 4 * inch
      vehicle_mass = 1000 * kg
      
      rim_height = 2.5 * inch
      
      tire_width = 175 * mm
      profile = 70 * percent
      wheel = 15 * inch / diameter
      pressure = 2 * atm

      REM Calculations
      REM ------------
      
      tire = wheel + profile * tire_width
      mass_on_wheel = vehicle_mass/4
      
      angle_to_kerb = ACS((tire-kerb_height)/tire)
      kerb_distance = tire*SIN(angle_to_kerb)
      mean_effective_area = tire_width * kerb_distance / 2
      
      rise = kerb_height - rim_height
      
      force = pressure*mean_effective_area
      acceleration_upwards = force / mass_on_wheel
      
      rise_time = SQR(2*rise/acceleration_upwards)
      
      speed = kerb_distance / rise_time
      
      PRINT "speed is ", speed/mph, " miles per hour"

This one gives me 7 1/2 miles per hour, with the speed increasing if the vehicle is heavier, kerb higher, rims lower, etc. I would NOT trust the figures. I just did this for amusement and I'm posting it as I doubt there will be anything else posted of a predictive nature.

It looks worse than it really is. It is just 10 lines of calculations and a PRINT statement.

I think the main factors are the kerb height and how far the rim is from the ground as these determine the height the wheel has to go up for the rim to miss the kerb. If the rim is already near kerb height, the car can go faster than with a high kerb and rims almost on the ground.

And, in practice, was the kerb hit straight on?
I wonder if this is a case of a wife bending a wheel and telling the husband she wasn't going that fast? You certainly shouldn't use my estimates for anything professional. Did I say that? Careful! I'll get my own post pulled!

 

[gerhardf]

This isn't the case of a wife, but close

I have been in (deep) potholes, ran over rocks, with reasonable speed, and never managed to damage the rim severely. This is the worst I've ever seen in front of me (but I'm not having much experience with this sort of thing). The whole situation, how it exactly happened, is a bit unclear, and I wanted to see whether I can get an answer of the type "yes, that's possible to happen at 30 km/h" or "this takes at least 60 km/h".

But I guess the variables are too many, and from what I've read so far it seems likely that the possible speeds -- even with all the data points I have and conducting the tests needed to get any sort of precision -- include a range that's so wide that it wouldn't help me much.


crysta1c1ear, if I read your code correctly, the speed that you are estimating is the speed where the kerb starts to touch the rim. The speed for a given damage would then be higher. Is this correct?

Gerhard

 

[GregLocock]

Very much depends on the height of the kerb and the angle at which it strikes and the speed and whether the wheel was locked.

Somewhat affected by tire profile and pressure (not so much for typical variations in pressure).

Very much affected by details of the construction of the wheel - if it was a low pressure diecast or gravity cast aftermarket alloy wheel then I would not be in the least surprised if it fell apart.

There are subtle geometrical features on a wheel which can substantially improve its kerbstrike performance.

Also, aftermarket, and many production, wheels are rarely heat treated.

There is an Australian Design rule that more or less specifies a performance for this sort of event, passing it is not necessarily a no-brainer, and the company that I work for has a much harder requirement to meet.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[crysta1c1ear]

crysta1c1ear, if I read your code correctly, the speed that you are estimating is the speed where the kerb starts to touch the rim. The speed for a given damage would then be higher. Is this correct?

Yes, I've estimated the tire size from the wheel size and tire details. I've subtracted the rim height from the kerb height to see how much the wheel needs rise for the rim to miss. There is some trigonometry to estimate how far the wheel has to travel from touching the kerb, to passing directly over it. The wheel needs to accelerate upwards fast enough for the rim to rise over the kerb. I've estimated an average tire area on the kerb and multiplied by the tire pressure to get an approximation of the upward force and divided this by a mass to see what sort of upward acceleration the tire on the kerb might be able to create.
Then I've determined how long it would take for the wheel to get high enough to just clip the kerb if it accelerated upwards that quickly. Finally I calculate a speed at which the rim might get just high enough to miss as it passes vertically over the kerb.

I did it as an exercise to see if my numbers came out as highway speeds, crawling speeds, or something that I thought were realistic, and - if the numbers looked real - to play with them to determine which parameters made significant changes.

The height from the ground of the kerb and rim play a pretty significant role I think. If the kerb is only just higher than the rim I think it is easy to get over it and one could go a moderate speed, whereas if the height difference is significant it is going to be hard to get over it and you'd need to drive slowly.

==

In my youth, I once thought that I would just miss a little traffic island. The car was slightly wider than I thought and I clipped the wheel on the kerb of the island. I think I was overtaking at the time. Probably only the edge of the tire really went up the kerb and I think that would be less effective at missing than hitting it full on. I don't remember the damage to the wheel, but I remember the damage to the steering. The car pulled to the side afterwards.
If the car pulls to one side you might be able to determine something about how the wheel hit the kerb from which way it pulls.

It was the driver's side wheel.

This isn't the case of a wife, but close

It was my father's car. ;-)
I didn't fully explain what happened, but they didn't have bulletin boards for him to investigate, thank goodness. Funnily, he was way ahead of his time. He died over twenty years ago, but predicted the internet, and when somebody asked him a question about democracy once, he rather oddly said "let's see what happens to Yugoslavia without Tito".