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Nerd alert: Newtonian physics, manholes and cycling
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 Content Alert: Newtonian physics, manholes and bikes


The other day on the road, a group of friends rode past a manhole without cover. We easily avoided it but it got us thinking that it would hurt pretty bad to hit it straight on without seeing it first.

So we asked ourselves how fast we would need to go to not crash riding over an uncovered manhole on the street.

The problem is that we can’t agree on the math and the simple math gives an answer that is hard to believe.

The simple math would have you fall into the hole by simple gravity only, for the duration you ride over the hole. The faster you go, the less time you have for your wheel to fall into the hole. So by the time you hit the end of the hole (the far lip) with your horizontal travel, if you travel fast enough, your front wheel won’t go down enough to cause you to endo.

So what is that speed you need to go to to avoid an endo?

Here is the simple math computation:

Assumptions: cannot fall more than 3cm into whole otherwise crash. manhole is 1 meter across. Assumes rider is unaware of hole, so no dynamic forces to try to unweight the front wheel or bunny hope.

How much time an object needs to fall 3cm:

t=square root(2D/g)
t = 0.0782195453699 seconds

Speed needed to cross 1 meter under that t time

s = d/t

s = 1m/0.0782195453699s
s= 12.78 m/s
s = 28.6mph

So in ideal conditions, ignoring friction and dynamic moves, you should survive if you go faster than 28.6 mph.

With 2cm max assumption, that is ~35mph minimum speed.

Feels like we would need to go faster to not crash or I screwed up my math.

Is my math correct?

Is it much more complicated than this? My friend feels you fall faster into the hole because the rider has his weight on the front wheel. And than the wheel rotation and pivot with back wheel may cause front wheel to fall faster into the hole.

Thoughts?

Thanks.
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Hello flafonta and All,

Test your hypothesis ... for safety considerations start the series of tests at 30 mph (to give you a decent margin of error) and be sure to film the results and post here later.

Oh .... and be sure to use a test dummy for the first runs.

After some thought try it without a rider first time .... just get the riderless bike up to 30 mph and run it across the manhole.

Get the test bike from one of your friends.

After some more thought .... create a long plywood ramp with a 1.2 inch lip at the end so you can roll over the end on to the road surface.

Measure the touchdown point from the 1.2 inch lip for the front and back wheel .... which will give you a fairly accurate indication of whether the front wheel will clear a 1 meter distance with 1.2 inch drop.

Of just ask Slowman as I think he has had practical experience with this very same situation.

Cheers, Neal

+1 mph Faster
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Did you do anything to help remove or reduce the risk presented by the hazard?

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Re: Nerd alert: Newtonian physics, manholes and cycling [AlexS] [ In reply to ]
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What, like put a trampoline at the bottom of the hole?
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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One could test this theory with a basketball/ soccer ball to see similar trends. The same principal happens in golf frequently.
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Based purely on experience, and not having attempted to validate your math, it seems improbable. There's a long descent near my house where I routinely get >35mph. At the bottom of that descent there's a fire station and in the street in front of that fire station there are several manhole covers and various other "utility" covers. Last summer, one of the covers on the utility lines, which couldn't have been more than 12" diameter, was missing. I didn't see it until I ran over it at full speed. The resulting impact was so strong that it launched one of my bottles (mind you, this was on a road bike) and the noise was so loud I thought I'd cracked the frame. I can't imagine clearing an opening 3x as large without at least completely destroying the front wheel.
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Re: Nerd alert: Newtonian physics, manholes and cycling [jkatsoudas] [ In reply to ]
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Reading these responses and talking to a few other cyclists, it feels like 3cm is way too much at speed. And the smaller the bump you can tolerate, the faster you need to go, therefore the smaller the bump needs to be, vicious circle. But it should converge eventually.

At 1cm max with the math above, you would need to go at ~50mph, which feels more reasonable. But then again, at 50mph, that 1cm bump will create quite a bit of force, likely damaging the wheel (and maybe the rest of you and your bike).

One other aspect: although the math above does not need to include the weight of the system (bike + cyclist), the damage your wheel/bike will get from the bump is probably proportional to the weight of the system. A light rider may survive a 1cm bump at 50mph, but a 250lbs Clydesdale may not.

Thanks for all the responses so far!
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Re: Nerd alert: Newtonian physics, manholes and cycling [Sausagetail] [ In reply to ]
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Sausagetail wrote:
What, like put a trampoline at the bottom of the hole?
There are many options, such replacing the cover if it's available, warnings of various kinds to prevent people hitting it or to avoid it until it is fixed, contacting the relevant road authority to also advise of a serious risk of harm so that road repair crew can get it quickly fixed.

Having had a leg amputation resulting from hitting a roadway hazard that someone had prior knowledge of but did nothing about, I feel my question is reasonable.

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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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flafonta wrote:
Is my math correct?
Math looks correct but allowing 3cm is like hitting one of those steel plates 3cm thick at 28mph. Seems like you'd be certain to pinch flat and likely damage your rim unless you were running very wide tires.
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Personal thought is that you’d have to account for the fact that you normally ha e two contact points on the road, and when the front wheel enters the hole, only the back wheel would support the bike. So you’d get a torque moment that would tend to rotate the nose down. Meaning you’ll smash the front rim into the other side extra hard. More Eulerian equations than just Newtonian.

Of course theory is one thing and practice is another. So go test it for us
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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I would think that with such a high velocity, the impulse would be exceptionally high, especially with a lip and/or the body geometry of the hole. The wheel deformation would be pretty violent and I think 3 cm is way to much. I would think that you would need under like 1cm of differential to get out on the other side relatively alright. any more than that and I would think you would be flying off with an exploded wheel.

Perhaps consider like 1/4 of the tire diameter as the drop (ie max impact causing critical deformation) before the impact would be too violent. Math seems correct
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Math aside, my thoughts after reading all these responses is that I don’t want to be the test pilot on the first run. Of course I decided to YouTube bicycle over open manhole cover, and best I could come up with was this unfortunate fellow in a car when the math wasn’t in his favor:


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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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its like a real-life middle-out scene
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Re: Nerd alert: Newtonian physics, manholes and cycling [IL2tri] [ In reply to ]
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IL2tri wrote:
Math aside, my thoughts after reading all these responses is that I don’t want to be the test pilot on the first run. Of course I decided to YouTube bicycle over open manhole cover, and best I could come up with was this unfortunate fellow in a car when the math wasn’t in his favor:


Crazy video. It's pretty incredible how something so simple can cause so much havoc.

FWIW the dynamics of a car situation are different in that the suspension is partial compressed by the weight of the car.

Therefore, with the unloading of the tire the spring will force the wheel toward full extension. This places the point of contact higher up the tire (effectively as if you were riding slower at the man-hole cover)

Suspension like this is good for keeping contact / control with undulating surface changes, but perhaps not so good with square-edge impacts.

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Last edited by: xtrpickels: Nov 30, 17 7:19
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Re: Nerd alert: Newtonian physics, manholes and cycling [xtrpickels] [ In reply to ]
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xtrpickels wrote:
Crazy video. It's pretty incredible how something so simple can cause so much havoc.

FWIW the dynamics of a car situation are different in that the suspension is partial compressed by the weight of the car.

Therefore, with the unloading of the tire the spring will force the wheel toward full extension. This places the point of contact higher up the tire (effectively as if you were riding slower at the man-hole cover)

Suspension like this is good for keeping contact / control with undulating surface changes, but perhaps not so good with square-edge impacts.

Your arms are your suspension - same principle applies. Once you ride over the manhole the stored potential energy in your bent, springy arms will be released, pushing the front wheel down.

A test-dummy might survive since he won't exert stored energy on the bars. However, a real dummy would not.

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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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Another factor to consider is the angle at which the wheel contacts the far side of the lip of the hole. Most of the discussion has implicitly assumed that the wheel would hit the far side perpendicular to the edge of the hole. But that's only one of many possibilities. Any other impact angle will produce a steering moment that will likely put the rider down on his/her side (immediately I would expect).
Something fun to think about...
Jim
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Re: Nerd alert: Newtonian physics, manholes and cycling [flafonta] [ In reply to ]
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I'm assuming it's spoiling the fun to consider what one would do if they had reaction time, correct? Not to derail, bikes are not the same as locomotives on tracks, or even cars on highways.

To be clear though, I'm impressed by your calculations from a theoretical perspective!

Case in point: I once had a very large dog run out in front of me while motorcycling in the dark on a two-lane road. I saw it about 2 seconds before I hit it. Had I hit it without reaction, I would be dead or nearly dead as I was traveling at about 55mph, and his back was probably as high as the front tire. The only thing that saved me was that I released the pegged front brake right before impact, which suddenly decompressed the suspension to full extension, and that got me barely through/over the dog. I still can't believe that worked. Even the slightest up-unweighting would make a man-hole cover a different physics picture.

But assuming you did not react, you'd be toast. That car video was nuts.

Matt
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Re: Nerd alert: Newtonian physics, manholes and cycling [gregf83] [ In reply to ]
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Yes, the math is correct.

On the other hand, the front wheel is not free falling into the man hole, because it is part of the rest of the rigid bicycle (frame, rear wheel), which are still outside of the manhole cover, thus the front wheel sort of pivots into the hole, rather than a true free fall, thus the actual speed necessary to traverse it (given the rim does not collapse/bend) safely might be less than calculated (based on a 2 minute review of this by a physics professor I know, not me.)

Two wheels good. Four wheels bad.
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Re: Nerd alert: Newtonian physics, manholes and cycling [DrTriKat] [ In reply to ]
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Yes, the speed with which the wheel falls will be less than a free-falling body, but if your professor friend thinks about the forces involved he will conclude the difference is negligible in the first few cm of free fall.
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