Looking for a formula for damage when sliding to a stop

[questionslide]

TL;DR Summary

When you fall and only slide for a couple of feet, there's usually major damage, while it's common to come out unscathed when you just slide on and on.

I'm looking for the formula that describes this.

The context is going down a hill in rollerblades: when people fall and they come to a quick stop (due to not having protective gear and there being lots of friction), they always end up with major injuries, while people with protective pads can sometimes fall and slide for 60+ feet and often be able to stand up and continue without a single injury.

Clothes and pads can obviously protect against road rash, but I'm certain that what's making the biggest difference in all of the falls I've seen or experienced myself has been the sliding distance, and I would like to make an argument for the use of protections based on this.

For that purpose, I'm trying to find the name of the equation that explains this, which in my head looks something like:
Impact strength = speed/sliding distance

While searching, I was looking at the physics of going down a slide, because I think it's a similar logic: due to there being very little friction, you can go down a massive water slide without hurting yourself, but I mostly found results that seem to include things like gravitational fields, which I'm not sure are that relevant in my scenario.
I know very little about physics, so I'm likely simply using the wrong keywords while searching.

Thank you.

 

[Drakkith]

Clothes and pads can obviously protect against road rash, but I'm certain that what's making the biggest difference in all of the falls I've seen or experienced myself has been the sliding distance, and I would like to make an argument for the use of protections based on this.

I'm not quite sure what you're trying to get at. The biggest factor in whether you sustain injury or not is wearing protective gear. It just so happens that protective gear often has less friction than skin does, which would explain why you can slide far longer before coming to a stop. Where sliding distance comes into play is that the amount of damage sustained by either your gear or your skin is proportional to the distance you slide, with some caveats regarding differing composition with tissues and gear/clothing layers (which really don't matter much). Your gear is just much, much more durable than skin is, which is why it protects you.

 

[jrmichler]

Having done face plants both on concrete while running, and on ice while ice skating*, I can understand your question.

Here's my reasoning, starting with the simplest case. A fall on a slippery surface has only vertical force. A fall on a high friction surface has the same vertical force plus horizontal force from the friction. The total force is the vector sum of the vertical and horizontal force, so the fall on the friction surface has higher total force. It does not matter if the surface is slippery, or if the protective gear is slippery. The result is the same.

Second simplest case: Protective gear has padding, which reduces the impact (vertical) force.

Third simplest case: Friction forces pull body parts out of position. This can be bad for, say, kneecaps.

*At about age 60 right in front of the Polish Palace bar (it's for real, look it up). Fortunately it was at a slow time, so did not entertain too many people.

 

[sophiecentaur]

TL;DR Summary: When you fall and only slide for a couple of feet, there's usually major damage, while it's common to come out unscathed when you just slide on and on.

I'm looking for the formula that describes this.

I know very little about physics, so I'm likely simply using the wrong keywords while searching.

Commiserations. This is a problem for you because Sports injuries, sports performance and also motor vehicle incidents don't lend themselves to analysis with basic Physics. In the case of injury or damage, the only way to resolve things seems to be with a court case. 'Expert witnesses' do battle to convince a jury which side is right in any claim. PF is pretty much useless for you about this - sorry.

There are loads of statistics and opinions to be found on various internet sites, which will be frustrating with expensive solutions, mainly. The only way to minimise the probability of injury is to use 'suitable' protective gear but every accident is unique so there's no guarantee you will be immune from danger. Manufacturers do not, as yet, offer a reactive force field suit for all activities.

The only way to avoid injury is to sit in a chair but that will give you heart problems and a bad back.

 

[Ibix]

I agree that the maths for this is complicated, but there are some things that can be said.

The old aphorism is that it's not the fall that kills you, it's the sudden stop at the end. The same applies going horizontally at speed - it's the slowing down that hurts. Essentially, the kinetic energy has to go somewhere, and it gets dissipated as friction (heating you up) or in deforming your body (tearing skin or breaking bones). And that happens more if you slow down fast: if you stop in a few inches it's pretty much the same as slamming into a brick wall.

Armour means that the energy is dissipated into the armour instead of you, and it's designed to be tough enough to take the punishment. Actually, the armour probably doesn't care if you slow down rapidly, but slowing rapidly is likely to cause you to flip and that's a risk for snapping something that's sticking out, like an arm or a neck. So letting you slide is a smaller risk.

 

[berkeman]

Welcome to PF.

I'm looking for the formula that describes this.

For that purpose, I'm trying to find the name of the equation that explains this, which in my head looks something like:
Impact strength = speed/sliding distance

This is not really a cause-effect relationship. The cause is the use of low-friction materials to lower the horizontal impact forces, which coincidentally increases how far you slide.

The old aphorism is that it's not the fall that kills you, it's the sudden stop at the end.

Exactly. As JR mentions, the vertical distance you fall still adds to the forces you experience when hitting the ground (like if you crash off the high side on a motorcycle, which flings you at least a few feet in the air before you come back down and impact the ground). But if you fall off the low side of a motorcycle, you basically end up on the ground without a lot of impact forces. Unfortunately, you may be traveling quite fast horizontally still when this happens.

So that's why motorcyclists typically wear leathers or low-friction ballistic nylon Gore Tex® protective suits, along with leather gloves and leather/plastic boots. The gloves especially may have extra impact/sliding protection like metal or plastic dots on the palms and backs of the hands.

BTW, the low-friction sliding part of a crash can take longer than you expect before you stop. When you low-side at 90+ miles an hour going into turn 5 at Laguna Seca Racetrack in Monterey, for example, you really need to count to 5 after you think you've stopped sliding before you try to stand up. Don't ask me how I know this...

https://www.express.co.uk/sport/oth...nnone-Suzuki-Sachsenring-Germany-Moto-GP-News

 

[sophiecentaur]

So that's why motorcyclists typically wear leathers or low-friction ballistic nylon protective suits,

What sort of cost? Also, how flexible for a skater doing stunts?
It's a scary business coming to a halt at those speeds. The videos are unbelievable.

Amazing that so many riders and skaters use minimal protection. Basically, any sums are teling people "No"

 

[DaveE]

For low speed stuff, most of that protective gear is aimed at reducing really unpleasant, but superficial, injuries. Yes, it's really unpleasant scraping the skin off your palms. So if your not wearing gloves and such while riding bikes/scooter/skates, your kind of an idiot. OTOH, me and my two orthopedic surgeons will tell you they don't help much for more serious injuries*. Skin heals pretty well, knees joints are likely to never be completely fixed.

I'd bet you see more serious injuries in Football than Rugby. Some protective gear just encourages stupider behavior.

* except for appliances with support, like the wrist guards I wore with the metal bar. I bet I would have had a broken wrist at some time without them.

 

[berkeman]

What sort of cost?

Full motorcycle leathers, boots, gloves will run about $2000, and a good street helmet will be $500-$750.

Also, how flexible for a skater doing stunts?

You wouldn't wear leathers for skating, but that's probably not what you are asking. When I inline skate, I wear gloves, elbow and knee pads and a bike helmet. If I were to try any stunts (unlikely), I would probably at least wear one of my motocross jerseys with long sleeves to hopefully cut down on road rash.

 

[berkeman]

BTW, one very important point to mention when talking about road rash is that it's especially important to protect joints that do not have much tissue around them. That includes ankles and toe/finger knuckle joints. The issue is that if you get road rash in areas that have plenty of tissue (muscle, fat, etc.), potential infections can usually be successfully treated with antibiotics. But infections in areas close to joints can result in joint infections, which are notoriously hard to cure.

(I learned this from my doc one time after she was checking me out after a moderate speed low-side crash on my street motorcycle. She was glad that I had good quality racing boots on, even though I was just commuting. If I had just had street shoes on, she said that I likely would have scraped up my ankle pretty badly, which could have resulted in one of those difficult-to-treat infections.

Your PSA for today...

 

[questionslide]

Thank you for all the replies!

"It's not the fall that kills you..." got me thinking. Could sliding on the ground like on the motorcycle example be considered a collision over a really long distance? Or does a collision necessarily mean head-on impacts?

I found the following formula: F=(1/2d)mv²
m=mass, v=velocity, d=distance,

That seems close to what I had in mind: the resulting force is reduced by the distance, but I don't know if it means what I think it does.

------------------------------

As for leather, it's actually used for IDH (inline downhill).

 

[Drakkith]

"It's not the fall that kills you..." got me thinking. Could sliding on the ground like on the motorcycle example be considered a collision over a really long distance? Or does a collision necessarily mean head-on impacts?

I wouldn't consider sliding a collision, no.

I found the following formula: F=(1/2d)mv2
m=mass, v=velocity, d=distance,

That seems close to what I had in mind: the resulting force is reduced by the distance, but I don't know if it means what I think it does.

I'm not familiar with that equation. It looks like the kinetic energy formula but with an extra term for distance.

You're actually looking for the wrong thing here. You don't care about the force applied to the body, that's going to be roughly the same for any slide, regardless of distance, as long as you're wearing the same gear and you weigh the same. If you're wearing the same gear and you weight the same, then three different slides of differing lengths will have the same force, since the force of friction is dependent only on the coefficient of friction between the you and the surface, and your weight: $f_k = μ_kF_n$, where $f_k$ is the force of sliding (kinetic) friction, $u_k$ is the coefficient of sliding friction, and $F_n$ is the normal force (equal to the force pushing you down against the surface, which is just your weight if we assume a flat, horizontal surface).

You're also not really worried about impact 'strength' either. That certainly helps determines the severity of a fall injury, but you've stated your more interested in the resulting slide, which is dependent on your horizontal velocity, your mass, and the coefficient of friction between you and the ground, not your vertical velocity or the impact force. Although, a higher impact force can lead to a MUCH higher friction force for the first few fractions of a second of a slide.

So if it's not the friction force on the body, and it's not the impact force, what should you be looking for? Well, in the context of people falling and sliding, what you're mainly looking at is how fast you're going and if you're wearing protective gear. Moving faster means you have more kinetic energy that needs to be dissipated. A simply vertical fall with little-to-no horizonal velocity will not involve sliding and will only result in an impact injury. Moving slowly will mean that very little kinetic energy needs to be dissipated and the slide will only result in minor injuries. Think of falling while running and skinning your palms. It hurts, but it's not a bad injury.

Falling while moving a high speed, say when skating quickly downhill or falling from a motorcycle, can result in serious injury from sliding on the ground. You can lose entire muscles and grind away your body all the way down to bone in the worst cases.

Wearing protective gear tends to increase the length of a slide, but that's not really what they were aiming for when designing the gear. As I already said, protective gear like elbow and knee pads or the outside of helmets tend to have lower coefficients of friction because they are hard, durable materials and not soft, squishy skin that likes to 'stick' or 'catch' on the ground. Other gear, like leather jackets, pants, or gore tex suits may or may not have similar coefficients of friction to skin, and may or may not result in a slide of different lengths compared to a no-gear slide. I don't know.

Really, I think trying to relate slide length with injury is not the right way of looking at things unless you are comparing slides of similar people wearing similar gear. And it's certainly not true that a longer slide results in less injury, all other things being equal. If anything a longer slide would imply a higher velocity, more energy that needs to be dissipated, and thus a worse injury.

 

[DaveE]

As for leather, it's actually...

... a good clue that your about to engage in a stupidly dangerous activity. JMHO.

Not that that would have stopped me a few decades ago. Thrills don't come cheap.

 

[Nugatory]

I'm not familiar with that equation. It looks like the kinetic energy formula but with an extra term for distance.

That's exactly what it is.
We have $W=Fd$ so if we're going to dissipate $W$ joules of kinetic energy over a distance $d$ we're going need an average force $W/d$. This does assume uniform deceleration, but that's a reasonable assumption for back-of-the-envelope calculations across a wide range of real problems.

 

[Lnewqban]

... For that purpose, I'm trying to find the name of the equation that explains this, which in my head looks something like:
Impact strength = speed/sliding distance

Sliding distance is the skater friend only if within that distance:

-A solid massive object is not impacted, like a car or guardrail.

-The generated erosion and heat by contact with pavement can't reach non-protected parts of the body.

-Sliding does not evolve into a continuous roll over motion.

The full-face helmet of the skater in this video saved his jawbone from impact against the road (neck muscles are too weak to control the head movement in these circumstances).
The cotton jeans did nothing to protect his legs.

 

[sophiecentaur]

I'd bet you see more serious injuries in Football than Rugby.

The two sports are surprisingly different. Heading a football has at last been acknowledged to produce long term effects like dementia but there are few head to head / body clashes in football compared with in Rugby. Leg injuries are common in both sports; it seems that no one has an intact cruciate ligament. Nearly all sportspeople pay for it later, requiring new knee joints after they pass the age at which their body was designed to pack up.

Elite Rugby players now wear smart mouthguards which record shocks to the head and a player will be taken off for examination. Likewise, the laws about tackling and scrums have become tighter and tighter, to reduce danger of spinal and head injury. But what can you do when the forwards are so huge and so strong? I'm always amused by the obsession that rugby players (pundits, in particular) have with the rules - it's a sport in itself. Brian Moore is my favourite arguefier; great fun to listen to on TV.

But it's diffferent for speed sports, in which accidents could so easily be reduced in seriousness by going at half speed (lol).

 

[Nugatory]

The two sports are surprisingly different. Heading a football

You have fallen into the linguistic divide that lies between Britain and America. @DaveE is talking about American football, you are thinking of the game that Americans call “soccer”.

 

[sophiecentaur]

yep. You're right!
I agree about the body armour being a waste of time - except for the dressing up fun it provides. Appropriate rules give better safety than padding and helmets but allow players to be strong and fit.

 

[berkeman]

Here's another use for leathers in MotoGP motorcycle racing -- They can be used as a brake on the front tire of the racer next to you to try to slow them down in corners...!

This last weekend at the Spanish Grand Prix in Jerez Spain, Marc Marquez invented this move as he was trying to pass Franchesco Bagnaia for the lead with two laps to go. Marquez managed a late-braking pass into a turn, but Bagnaia passed him back on the inside of the subsequent turn. The picture below shows Marquez leaning into Bagnaia's front tire and using the leathers covering his right shoulder against the front tire of Bagnaia's Ducati. Unfortunately, the leathers were too slippery, so not much front braking force was generated and Bagnaia led coming out of that turn.

Marquez was quite proud of the tire marks on his shoulder, though, showing them off after the race (where he finished 2nd behind Bagnia):

Kids -- don't try this at home!