Impact Speed

[Dan B]

I think that Green1 is probably right, although he didn’t really explain how he reached his conclusion. Others may have also reached this conclusion but I couldn’t be bothered to read all the posts It is all about vectors as someone has already stated. Imagine a right angled triangle with the forward speed of 20 mph represented by the long side and , say, 10 mph the vertical speed of your head, by the sort side. The hypotenuse represents the speed that your head will hit the tarmac, which is the square root of the sum of the squares of 20 and 10. ie 400 + 100. Square root of 500 is about 22.3. I might be totally wrong as it is a long time since I failed to pay attention at school, but seems logical to me. However, if you pay attention to your riding, rather than trying to solve questions like this when you are out cycling, then you probably will never find out whether I am right or not.

Your calculation is correct (well, I assume it is, it looks like it should be) but your reasoning is still wrong. If the correct answer (horizontal and vertical are independent, as green1 has said) seems unintuitive, think about angles. You might be travelling at 22mph when you hit the ground but you hit it at an angle and slide - it's a glancing blow. The faster you are travelling horizontally or the slower vertically, the more glancing it is - until, in the limit, at 0mph vertically you don't hit it at all and merely skim it forever - in that case you can see quite clearly that the horizontal component makes no difference at all to impact speed because there is no impact when you're travelling parallel with teh ground. It's the vertical component (strictly, the component perpendicular to the ground, if there are hills, humps, or kerbs involved) that's the relevant bit

(Friction, now, that's a separate issue. If the helmet rubs against the ground and stops very quickly, or even worse catches on something instead of sliding, that's when you want to start worrying about horizontal speed)

 

[ufkacbln]

Why not just turn the handlebars and avoid the wall?

 

[Twilkes]

Why not just turn the handlebars and avoid the wall?

Because that's where the cycle lane goes.

 

[russ.will]

I think what you hit and the way you hit it, are at least as important as the velocity - Punch me in the head and it will hurt. Punch me in the head with a knuckle duster and it will crack my skull.

I've 'got off' several motorbikes on track days at 70mph+ speeds and bounced a bit. The only serious injury was to my wallet. A friend at work who time trials with a cycle club, fell off at standstill, hit his helmeted head on a kerb edge and ended up with a skull fracture and black and white vision for a week. Anecdotal, yes, but a kerb edge with a 6ft drop could have killed him.

Russell

 

[deanE]

Your calculation is correct (well, I assume it is, it looks like it should be) but your reasoning is still wrong. If the correct answer (horizontal and vertical are independent, as green1 has said) seems unintuitive, think about angles. You might be travelling at 22mph when you hit the ground but you hit it at an angle and slide - it's a glancing blow. The faster you are travelling horizontally or the slower vertically, the more glancing it is - until, in the limit, at 0mph vertically you don't hit it at all and merely skim it forever - in that case you can see quite clearly that the horizontal component makes no difference at all to impact speed because there is no impact when you're travelling parallel with teh ground. It's the vertical component (strictly, the component perpendicular to the ground, if there are hills, humps, or kerbs involved) that's the relevant bit

(Friction, now, that's a separate issue. If the helmet rubs against the ground and stops very quickly, or even worse catches on something instead of sliding, that's when you want to start worrying about horizontal speed)

The question was "what speed would my head hit with the ground?”, not whether it would hurt.

 

[StuartG]

I'm not sure where this is going. Look if i drop you head first from 1.5 metres you will die a dreadful death not so much because of the speed of impact as the mass behind. Your body will crush your skull (and the helmet). If I drop you from a horizontal position then your head/helmet will strike the ground at the same speed but the helmet/skull has only to dissipate the energy in the head - much smaller and maybe avoid any crushing injury. Actually because the impact will be different along the body the difference will put a strain on the connecting bit - so neck injury may be more relevant.

That's supposing you were unconsious and took no defensive action. Mostly we do. Close to exception is on black ice where the fall is completely unanticipated limiting any mitigating action.

As I've said before most falls start with your head furtherest from the ground with a lot of gristle and bone between it and the hard stuff. Its the rotation, if any, of your body that is needed to put the head at risk.

 

[Crackle]

But say it takes 1 second from the bike wheels slipping from under me to my head hitting the tarmac - assuming that's a constant fall from 1.5m (which it might not be), then the speed will be around 1.5m per second, or 5.4km per hour. So not very fast. The forward speed would just affect how many more times I hit the ground, or how much my head got scraped.

I'm trying to think of ways that a head would hit the road at a much faster pace but I'm struggling.

Having said that, I'm not about to try this on my commute home. 8-)

Heh. I've tried this, many moons ago, probably at about 20mph and whatever speed it hits, it will probably crack your skull.

Anyway, what is commonly used to assess head impact is the Gadd severity index. Here's one someone prepared earlier.

http://www.smf.org/docs/articles/hic/Newman_Snell_presentation.pdf

Now if you can just fit the figures into the equation....

 

[green1]

the bullet thing, a 7.62mm weighs 150.5grammes dropped from 1.5m - takes 0.5second (though I think thats a computer minimum)
Fire a 7.62 @2750f/ps - has an absolute range of 5miles - takes 9 seconds to hit the ground.
the bullet flys absolutely straight, no drop for 0.32 seconds - 300yds

to achieve absolute range the projectile be it a bullet, shell, stone has to be fired upwards, usually at 45 degrees.
A bullet will drop in the first .32 sec but it will be negliable.

look up escape velocity - its about 11.2ft/ps its the speed were your kenetic energy minus gravitaional pull = 0

I suggest you go look at it again. It's approximately 11.2km/s

But say it takes 1 second from the bike wheels slipping from under me to my head hitting the tarmac - assuming that's a constant fall from 1.5m (which it might not be), then the speed will be around 1.5m per second, or 5.4km per hour.

Your right it isn't. Falling off the bike so it can be assumed vertically the heads initial speed is 0, acceleration is 9.81 metres per second per second and distance is 1.5metres, so:
Final Velocity(squared) = Initial Velocity (squared) + 2 x Acceleration x Distance or v(2) = u(2) + 2as

v(2)= 0 + (2x9.81x1.5)
v(2)=29.43
so v= square root (29.43)
v=5.42 metres per second (in the vertical plane, you need to then add the horizontal part)


On a side note if my kids ever need extra physics tuition someone remind me never to send them to Licramite.

 

[Licramite]

Hey at least my thoery was correct , if you could fire a bullet at 35481ft/ps it would defie garvity, having escape velocity. -
Interesting we came up with the same answer for the impact speed having calc'd it in two different ways.

 

[StuartG]

On a side note if my kids ever need extra physics tuition someone remind me never to send them to Licramite.

Is Licramite from the land that gave us Newton, Barnes-Wallis and the Physics 'O' level?
Some discrepancy methinks.

 

[green1]

Hey at least my thoery was correct , if you could fire a bullet at 35481ft/ps it would defie garvity, having escape velocity.

Indeed it would, for a few milliseconds then air resistance would bring it back to the ground rather quickly. And good luck finding a material sturdy enough for the pressures required to make the gun barrel.

 

[StuartG]

if you could fire a bullet at 35481ft/ps it would defie garvity

OMG Newton disproved (screws Einstein too). What next?

 

[Dan B]

What does the p in ft/ps signify? Pre-SI units are not my strong suit, sorry

 

[Licramite]

Is Licramite from the land that gave us Newton, Barnes-Wallis and the Physics 'O' level?
Some discrepancy methinks.

and the famous - secondary modern education

makes you proud to be British !

 

[Twilkes]

Well, I got what I wished for - bicycle slid out from underneath me coming off Glasgow Green this morning (<10mph so not too fast). People say that time slows down when you fall off your bike, but this was over with before I knew what was happening - wheels slid to the right, handlebars went down, and I'm not entirely sure how but I just kept on running! Skating away on the thin ice of the new day.

So the answer is 0mph. 8-)

(nb if I had ever switched to clipless pedals I'm pretty sure I'd be nursing a bruised hip and wrist this morning.....)