You should see the other guy (Appendix)

I tried, for about 60s, to think of a funny title for this, but, as you all can see, I came up dry and my PhD training kicked in...

So here are my attempts at describing the mechanics of a gormless bogger¹ falling from his bike...

What I am looking to do is calculate my velocity on impact against the post, based on my total energy going into the impact (my Kinetic Energy from forward travel, that I am assuming smoothly segues rotation about a point and my Potential Energy from falling a bit). I can then have a go at the force on my shoulder, when I had bumped against the hitherto upstanding Mr Post.

The first picture below is an artist's [This guy... I'm pointing at myself with both thumbs] impression of the subject (me) on his bike, with the measurements of the rear wheel radius, a guess of the bike's and my centre of gravity and a guess of my shoulder height (0.2, 1.1 and 1.5m respectively)

The centre of gravity is somewhere just over the seat of the bike (arbitrarily taken as 10 cm, giving a total[-ish] height of 1.1m for the centre of gravity.

From the inset: The gears and chain are housed- to protect the poor things from the elements, doncha know- so I couldn't count the teeth on the gears, which would have been far easier.... From some surreptitious eyeballing, I have:

• Pedalling period² (T_F)=1.5s
• Front gear radius (r_F) = 0.08m
• Rear gear radius (r_R) = 0.03m

Let's say the gear ratio is represented by the ratio of the gear radii (which would be valid if they had the same number of teeth per unit of circumference), then the rear wheel's linear velocity is calculated using the steps below:

It is reasonable enough to assume that the velocity of the wheel is the velocity of the bike and me; A point of the wheel doesn't really move when it is in contact with the ground; ergo the bike and I move instead.³

A quick look back at my goals... Velocity ["check"]

Now to the change in height... Of all my ropey assumptions, here is easily the ropiest of them: I'm going to assume that the bike and I were a rigid body.⁴ Which makes things incredibly convenient, since the relative positions between my shoulder, what was a wheel and now a fulcrum, and the centre of gravity don't change.

My shoulder goes from 1.5m to 1.1m in elevation, which is a change in height of 0.4m. However, for potential energy we have to look to the change in height of the centre of gravity. By similar triangles, drop in height of the CoG can be calculated:

The next step is the total energy calculation and the velocity of a point object in the position of my centre of gravity:

Unfortunately, calculations using centre of gravity give lumped answers; I don't know what the velocity of my shoulder was [and frankly I want to finish this post in the next ten minutes]. If I was being correct and rigourous^4.5, I'd do moment calculations with estimates of the distribution of my mass, based on that I can get an expression that will tell me the velocity at my shoulder.

Let's say that my shoulder velocity is 4m/s (more than the CoG velocity, I figured this was reasonable because it is far from the turning point and centre of gravity). That gives an applied force of 800±25%N (mass by change in velocity (4-0) divided by deceleration time [writing on my white board takes time - use your imagination]).

Now, according to the internet a broken clavicle⁵ is a common injury for falling off of your bike onto your shoulder [LINK].⁶ According to this publication peak axial compressive force (compression along the length of the clavicle) is 2.41±0.72kN (listed in abstract). However, the paper itself lists the fracture force as a much lower value: 1.91±0.84kN.

Let's say I am on the frail side, one standard deviation to be exact, then force to do me damage is 1,070N. So the odds of me doing myself damage from this were disappointingly low (unless my head happened to hit instead, but that's another story).

If my straw-house of estimates is anything to go by, I experienced about 8gs on impact and an impact velocity of about 9m/s is needed for an average clavicle to break. This works out as 32km/h, which is reasonable enough, and is inline with statistics on to severe injuries and fatalities in road accidents.

In reality, I am not a rigid body:

• There would be energy losses due to my body's plastic deformation as I fell
• My soft tissues (read: amply muscled shoulder) would have absorbed more of the energy

And also,

• The post broke, so there is no telling how much of the force I actually experienced.

Now, if you will excuse me, it is the 2nd of October and over 25°C outside. I've got some kung fu to do.

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¹Funny side-note, I grew up on "Bog Road"ⁱ - I saw nothing wrong with that until I went to Summer camp for the first time. [Spoiler alert] They laughed at me... Bad enough my home town is Lisdoonvarna [LINK 1,ⁱⁱ LINK 2ⁱⁱⁱ]
²The time for my right pedal to go through 360°. I estimated this from my nominal pedalling rate in instances after the fact: "it ain't 1s and it's less than 2s."

³Nothing new.
⁴Ooo-er vicar.
^4.5Not that the rest of it is particularly rigorous :/
⁵Am I the only person that finds this word rather lewd?
⁶OK, I am being a sophist here, but it's a convenient bone and it has a reasonable chance of being a common injury because it is such a wuss, in the area of interest and would be put under axial compression. This ain't peer reviewed :P

****

ⁱThe Fresh Prince has got nothing on me.

ⁱⁱI did not expect a Dutch article about Lisdoonvarna :/

ⁱⁱⁱA decided advantage of not being in Ireland is that this song  (heretofore known as my nemesis) is not known where I am.^A

°°°°

^APoint of note: Youtube has a new function that I noticed with this video; It listed Christy playing in Antwerp on the 5th October. How... convenient.