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# Calculating Impact Force on the Suspension of a Car in Potholes?

07/07/2011 4:55 PM

Actually,the above title is my project's subject . I'm not exactly sure how I can do the force analysis on the wheel and suspension system itself.

Would anyone please help me if you got any idea !!

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#1

### Re: Calculating impact Force on the Suspension of a Car in potholes?

07/07/2011 5:11 PM

Is this a school project?

I'm unaware of a direct formula, or even a set of formulas for this specifically... but...

You will need such info as:

• Speed of travel
• Geometry of pothole (specifically depth)
• Geometry of wheel (specifically radius)
• Weight, or load on the wheel
• Pressure in the tire (different pressures will absorb forces differently)

I'm sure there are other factors that must be considered, such as the gas precharge in the shock, spring rating etc.
I'm sure someone will come along with a bit more knowledge/time on the subject.

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#14
In reply to #1

### Re: Calculating impact Force on the Suspension of a Car in potholes?

07/08/2011 1:04 PM

Actually i have no idea about the subject, i just srated. i have to find a car model with all specification of suspension to be able to solve all equation regarding this project.therefore,my supervisior told me you can assume whatever you think is hard to find out. for exmaple depth of the hole 6 inch , car speed is 30 mile , the tire and acceleration ,etc can be assumed...

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#2

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/07/2011 9:07 PM

Do you not have any idea, at all how to proceed?

The aristocrat is telling you things that you must have already had an inkling of.

What have you done so far? How can we help you if you're not willing to at least tell us what you do know? Perhaps I should say, why should we help you.

If you were to hang around here, you would find that I am particularly unsympathetic to persons such as you who want the answers without (apparently) putting forth any effort themselves.

Good luck with your project.

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#3

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/07/2011 10:42 PM

Interesting query! I have wondered about such myself, but never did anything about them.

I imagine the impulse theory will get involved. As will the tire sidewall stiffness, inflation pressure, etc, etc.

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#4

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/07/2011 11:57 PM

Let us know how you are planning to proceed.

How deep into the pothole the tire goes has to do with the spring rate, the damping, the ratio of sprung to unsprung weight, the stiffness of the tire and the geometry of the tire and pothole, and to some extent, the direction(s) of motion allowed by the suspension linkage.

For simplicity, pick a single speed, a single pothole configuration, etc. Calculate what happens at several increments as the wheel enters the pothole. As the wheel drops, the suspension extends, and that corner of the car becomes supported less firmly, because the spring is extending. The car will start to drop at that corner with an acceleration that depends upon the difference between the weight at that corner and the force now supplied by the extending spring. Damping will also have its effect. Most dampers have more damping effect on rebound (extension) than on compression.

Read about the effect of spring rate on ride frequency, and the effect of various ratios of sprung to unsprung weight.

The wheel will experience some maximum downward speed, and the tire deflection, as the wheel stops moving down against the pothole bottom, will depend upon the mass of the wheel and tire and part of the mass of the suspension arms (the unsprung weight at that wheel).

Consider the wheel's downward acceleration at the instant that the road drops away, with different spring rates.

In most modern cars, there will be significant rearward motion of the wheel relative to the car body as the tire collides with the exit edge of the pothole. The elastic suspension articulation points permit this movement to reduce harshness.

If you have access to a high speed video camera, photographing a wheel traversing a pothole will help you understand what happens.

Interesting project. Let us know how it goes.

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#16
In reply to #4

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 1:09 PM

Actually i have no idea about the subject, i just srated. i have to find a car model with all specification of suspension to be able to solve all equation regarding this project.therefore,my supervisior told me you can assume whatever you think is hard to find out. for exmaple depth of the hole 6 inch , car speed is 30 mile , the tire and acceleration ,etc can be assumed...

the shape hole is square and the tire hits the sharp corner of the hole,

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#17
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### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 1:44 PM

Based on this statement, "you can assume whatever you think is hard to find out" why not just assume that the force will be 8,621 pounds.

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#18
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### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 2:16 PM

HAHA... Good one. I think the answer is ....42.

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#19
In reply to #18

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 3:08 PM

I can just see him at his first job interview.

"Experience? Actually i have no idea about the subject but there's this forum on the internet that usually does all my work for me. It's called CR4".

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#21
In reply to #18

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 6:24 PM

...and all this time I thought the answer was 54!

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#20
In reply to #16

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 3:22 PM

You could temporarily ignore the downward path of the wheel, and focus only on what happens as the tire hits the pothole edge and moves up. 6" is relatively deep (about the full depth of a tire section) and as a result, a significant part of the impact will be trying to deflect the wheel rearward relative to the car body. Initially, you can probably ignore this, too.

You can find both spring rate and wheel rate (spring rate as affected by suspension link geometry) examples on the web from the people who sell coil-over dampers to racers. Nick's suggestion of treating the car as non-moving in the vertical direction would be a good simplifying technique. Another simplification is to treat the spring as massless. In the very simplest case, the force on the wheel will be predominantly that caused by the wheel/tire assembly's inertia. The rate of acceleration will depend upon the effective spring rate of the tire. (You may find that the tire contacts the rim before the wheel can move out of the way... in that case, you could further simplify by making the hole less deep.) You may need to measure the effective spring rate of the tire empirically: its change in volume, and the force applied to the increasing area of contact as the tread deflects at the pothole edge is not simple.

Once you have the upward acceleration of the wheel without the suspension spring force in play, then you could add in the effect of the suspension spring force, and its change as the wheel moves. Then add in the effects of damping, and the smallish effect of the car body moving downward at the same time as the wheel is moving upward. With high rate spring, this downward movement can be pronounced, if the pothole is long, relative to the car speed.

Vibrations and flex in the car structure, waves in the suspension members... all that lies outside the scope of your project, I'd guess. You can, I think, consider the car's chassis and suspension members to be rigid.

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#5

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 12:11 AM

If this isn't a phD thesis then you are in way over your head. This is a 3 dimensional problem and the force pattern is not simple.

In these times we use modal analysis with computers to determine the forces. Why? Because the entire vehicle structure is flexible, has mass and an infinite number of vibration modes. The roadway surface also has these characteristics; but the are generally an order of magnitude less in the effect on the forces involved. The resulting problem is solvable by computer approximation. This is practical for most real world engineering problems. But a closed form solution is not possible.

A simple approximation in one dimension can be made using integral F*dt=m*dv with some assumption of linear relationships. Perhaps your project can consist of an exploration of the validity of this method for some real world examples.

I am no great mathematician but have used this approach a couple of times in my career to determine order of magnitude of a problem of a shock from an impact on a flexible structure. Perhaps an undergraduate level project can be framed to explore this. It is a topic few mechanical engineers have explored with analysis they preferring to instrument the subject with accelerometers employing expensive structural analysis test equipment and/or finite element software to attack the problem.

Ed Weldon

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#7
In reply to #5

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 5:23 AM

hmmm...I seem to remember installing a supercomputer for a "major auto manufacturer" to do things like this...hope the OP has one handy.

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#6

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 5:16 AM

This a very simplified model based on the fact that car inertia is a lot larger than the one the wheel with its support would present. Between wheel + support (Mw) and ground you have the tire stiffness (Ct) and between the car and the suspension the suspension stiffness (Cs) and the damper (Ds). This model is used for a first approach in suspension analysis. Now you can consider the ground profile as a sinus curve or as a ramp as you wish. You may consider the wheel as stationary in "x" direction and the "profile" moving with Vx . In the 1st phase the wheel will be accelerated downwards and if the depth is not over a threshold the "car" will not follow due to its own inertia. In the second phase the wheel is pushed upwards via the tire and against the damper.The damper has different damping effects in order to maintain the tire always in contact with the ground. However if the vertical profile velocity is too high the mobile equipment (wheel+support) cannot follow and the contact could be lost.

For low depth holes you may consider the "car" as an absolute reference without vertical movements. As I wrote above it is a simplified model. So that you write the equations fro the wheel and apply at the tire level (contact between tire and ground) a displacement function of the profile and the Vx value which gives the Vz value. This allows you to compute the "F" and the "R" which are the values you want to find. Of course you have to introduce the right values for Mw, C tire, C suspension and D suspension.

Good luck

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#10
In reply to #6

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 10:26 AM

Very good answer, albeit perhaps a little too direct (making it too clear and easy for the student).

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#11
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### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 11:20 AM

He has still to understand the system and write the equations and see how to solve them. What do you want not every body is able to give a good answer. Any way I prefer to show the path instead of being cryptic and give no hint. If he understood then he learned something and this is the final goal.

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#15
In reply to #11

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 1:08 PM

Actually i have no idea about the subject, i just srated. i have to find a car model with all specification of suspension to be able to solve all equation regarding this project.therefore,my supervisior told me you can assume whatever you think is hard to find out. for exmaple depth of the hole 6 inch , car speed is 30 mile , the tire and acceleration ,etc can be assumed...

the shape hole is square and the tire hits the sharp corner of the hole,

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#8

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 5:51 AM

I keep telling my wife, the faster I can get over the pothole (or speed bump) the less jarring of the vehicle that is felt. I don't think she believes me.

It does limit the amount of time I have to experience the obstacle and I don't spill as much coffee.

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#12
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### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 12:29 PM

This is an interesting subset of the generalized problem taking into account variables such as speed and width of the pothole in one direction, single degree of freedom response of the mass/spring/damper system of one wheel, diameter of the wheel and effect of tire pressure on the impact. Assume 90 degree edges of the pothole and infinite depth. ............Ed Weldon

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#9

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 8:34 AM

Start with the 3 conservation equations. Then derive from there.

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#13

### Re: Calculating Impact Force on the Suspension of a Car in Potholes?

07/08/2011 1:03 PM

Actually i have no idea about the subject, i just srated. i have to find a car model with all specification of suspension to be able to solve all equation regarding this project.therefore,my supervisior told me you can assume whatever you think is hard to find out. for exmaple depth of the hole 6 inch , car speed is 30 mile , the tire and acceleration ,etc can be assumed...

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