# Driver deceleration in a crash

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### #1 NeilR

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Posted 18 January 2014 - 11:34

I watched a crash recently...it wasn't planned, where a Formula car doing around 130kph (logged by the car) hit a largely loose rock wall on the outside of the track. The left front wheel took most of the initial hit; bent back into the tube, turned the nose around and into the wall, witht he nose cone compacting well. The driver had no HANS device and got away with a fractured wrist. What I am interested in is the theoretical forces on the car and driver, but in physics at high school I was far more interested in the bodacious shape of Sharon...well never mind, another story there I feel. In short my physics is rusty enough to count as a base element.

However if force on the car can be calculated is it correct to use Favg d = - ½ mv2 or Average force times distance = negative half mass times (velocity squared). Can I assume added distance for the driver due to belt stretch and body compression as well as car crush?

Regarding the deceleration, what would be a reasonable figure for the time for the impact? The onboard G meter recorded around 60G, which suggests that the impact took two seconds - it looked liked it took far less, so I must be overlooking something. Any ideas?

### #2 saudoso

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Posted 18 January 2014 - 11:55

Per your initial formula if it decelerated constantly over one meter you'd get 651,7 m/s2 (66.5g).

Now lets decelarate 651,7 m/s2 from 130kph which is 36,11 m/s. It'd take 0.05s to crush.

Seems right, where did two the seconds came from?

### #3 Joe Bosworth

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Posted 18 January 2014 - 12:08

Neil

Your calculation method for average deceleration is accurate.  The only problem in your problem is that you would have had at least three specific periods of differing decels.

The first would have been the initial decel of impact with the rock.  This will be affected by the mass of the rock and give in the car structure and the rock shifting.

The second would be controlled by the tyres sliding on the surface and if conventional track surface would be about 1,4 G depending on several factors. (Much less if off track.)

The third is the easiest to calculate if you know the impact speed of the presumably unyeilding wall.

For affect on the driver you, by all means must calculate the driver and restraints as a separate calculation within the car.

Here again you will have at least two differing values as the belts would have been unlikely to have gone to max stretch only once in this series of vehicle actions.

Compounding the answer to the problem is that you don't know the angle of any of the impacts.

Under any circumstances the 60G that you quote would not be an unusually found value for an incident such as you desribe. But even this finding is dependent on the mili-second calculation period in the meter's internal settings.

Good question but all but totally un-answerable.

Regards

### #4 NeilR

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Posted 18 January 2014 - 12:41

saudoso the two seconds...bit embarrasing...sorry I did not trust my own calculations as the number seemed so small and my own abilities limited, so I used this to get close to the 60G: http://www.smartconv...calculator.aspx which clearly was the wrong thing to do.

Joe, thanks for that, very instructive indeed. The track is a hillclimb track with a compacted natural soil wall, but 'soil' is a loose term in Australia as the available surface is 90% rock held together by dried clay and hope. The impact did scatter loose rock across the track, but I'm not sure what difference if any that would make. However I absolutely take your points about angle and un-answerable question. If I were to replicate the 60G tub load at a similar speed in a lab on a sled into a block of concrete, what sort of G load would be reasonable for the 'driver'. Clearly the belt stretch and body compression, would reduce some of the load.

BTW I feel that the car performed very well indeed and the driver was lucky. He is going to buy a HNR before running again, but the cost of repairs will slow him down a bit too!

Edited by NeilR, 18 January 2014 - 12:43.

### #5 NotAPineapple

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Posted 18 January 2014 - 14:58

For a rough guess of the average accel take this high school physics equation:

V² = U² + 2as

Solve it for acceleration and considering that final velocity (V) = 0:

a = -U²/(2s)

Where:

a = average impact acceleration in m/s²

U = impact velocity in m/sec

s = stopping distance in m

The stopping distance can then be made to be:

LengthCarCrashZone + LengthWallDeformation + LengthSeatbeltStretch + LengthForwardHeadMovement

Which will give you the average acceleration of the head. To find the average acceleration of the torso, calclate the distance without the forward head movment term. To get the acceleration as the data logger would read it, take out also the seatbelt length.

If I use an impact speed of 90km/h, a crash zone length of 600mm on the car and a wall deformation of 50mm I get 50g average. Which is in the ball park of the data acquisition (people always quote the peak acceleration from the data).

If you add in 100mm of seatbelt extension you go down to 42g. Then with 100mm of head movement you go down to 37g.

If you setup this calc in an excel spreadsheet and play around with it you will learn a lot about the importance of crash zone lengths.

Edited by NotAPineapple, 18 January 2014 - 15:10.

### #6 NeilR

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Posted 19 January 2014 - 10:27

thank you, that is an interesting way of looking at it. I had not thought of torso/head difference and the head number is rather frightening.

### #7 bigleagueslider

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Posted 20 January 2014 - 04:13

Stop and think about the injury that would result to a driver's neck/spine from a frontal impact with a max decel of 40g. If we assume the drivers head and helmet has a mass of 15lbs, the max force on his neck/spine would be around 600lbf. This type of injury is known as an internal decapitation, and many race drivers have died as a result of it.

In 1999 at the Laguna Seca Champ Car race, I was standing just a few yards away when Gonzalo Rodriguez lost control of his Penske/Lola, crashed head-on into a concrete barrier at around 140mph, and flipped up and over the barrier.  He was instantly killed due to an internal decapitation. It was horrifying to witness, and as soon as it happened I knew he was killed by the crash. Sadly, just a few weeks later I was standing in the infield at Fontana near the back straight watching the Champ Car race, and I witnessed Greg Moore lose control of his car exiting turn 2, skid across the infield grass, flip over, and finally impact the infield concrete barrier at high speed, killing him instantly.

The thing I recall from both of these events was the horrible sound of screeching tires followed by the sound of a carbon fiber tub exploding after impacting a concrete barrier. The HANS device should be mandatory in every form of road racing.

### #8 indigoid

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Posted 20 January 2014 - 04:45

The HANS device should be mandatory in every form of road racing.

Totally agree. Similar but not identical devices are now used in motorcycle racing as well.

There seems to be two similar injuries described on the internets - the internal decapitation as you mention, and basilar skull fractures as commonly mentioned in the usual motorsport fora, here included. I don't know anatomy well enough but they do sound very similar. Anyone know what the distinguishing points are, if any?

### #9 NeilR

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Posted 21 January 2014 - 11:41

I am increasingly concerned about the place that HANS has acheived and it's monopoly on the FIA device market. Note I have not issue with it's performance - though I'd like side impact protection.

### #10 indigoid

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Posted 21 January 2014 - 13:45

In 1999 at the Laguna Seca Champ Car race, I was standing just a few yards away when Gonzalo Rodriguez lost control of his Penske/Lola, crashed head-on into a concrete barrier at around 140mph, and flipped up and over the barrier.

At the top of the corkscrew, says Internet. I thought it might have been, though I've never been there and until now had only experienced Laguna Seca via console games... How often do people come unstuck in that spot? Considering the non-trivial crest there immediately before the left turn, I'm surprised that they still don't have substantially greater run-off area (or at least didn't in 2009 when this video was made, see 2:35 onward...)

### #11 bigleagueslider

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Posted 22 January 2014 - 03:48

The crash that killed Rodriguez occured on the section of track before the uphill straight leading into the corkscrew. He went off the track at the end of a straight at high speed, and the short run-off area ahead of the concrete barrier was just dirt. so his brakes were useless.

### #12 Sisyphus

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Posted 26 January 2014 - 19:07

Actually, Rodriguez hit the wall at the top of the hill at the entrance to the corkscrew.  Here is a tape of the crash--fair warning, it is an ugly accident:  www.youtube.com/watch?v=19FI1e79O1Y

I went off in a Formula Ford at almost the same place but fortunately at only about 70 mph and the nose just hopped up on the top of the tire wall.  Maybe only 30 g's or so and got away with a few stitches in my elbow.

### #13 Magoo

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Posted 26 January 2014 - 20:56

I remember the Rodriguez crash. Also Greg Moore. Saw them both.

The decels experienced by the head and body in an impact are so remarkably different from those of the vehicle that Dr Steve Olvey, CART medical director, organized a program in which accelerometers were installed in the driver's earpieces and then piggybacked as additional channels on the vehicle's IDR. I don't what became of the program or the data, however.

### #14 Motie

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Posted 06 March 2014 - 01:01

Here is some stuff that I wrote up a couple of years ago:  http://www.trackforu...-crash-survival