Change in throwing circle size

[eldrick]

i think a ballpark increase in throwing distance will be

~ (s1/s2)^1/2

brief workings :

acceleration across a small circle for a short period can be considered constant ( it likely isn't, but then you need calculus ), so from newton

v^2 = u^2 + 2as

u = 0

s = v^2/2a

s = circle diameter, v = speed of thrower moving across circle ( which we assume is directly related to release speed )

this boils down for a bigger circle to

v1/v2 = ( s1/s2 )^1/2

someone please check the circle sizes, but if it's 5' & you increase it to 6',

for a 19m SP'er -> 19 * ( 6/5 )^1/2 = 20.8m

for a 21m SP'er -> 21 * ( 6/5 )^1/2 = 23m

so we are getting on for 2m increase

for DT'er

for a 65m DT'er -> 65 * ( 6/5 )^1/2 = 71.2m

for a 70m DT'er -> 70 * ( 6/5 )^1/2 = 76.7m

so something like 6m increase

NB these increases will only hold for small increase in circle size - if your getting on to double it, it certainly won't hold

[imaginative]

An issue that complicates the matter considerably is where the speed of the
shot comes from. There are at least two components, when breaking it down
funcionally:

1. Speed of the jumper relative the ground (where your calculations probably
give a good first approximation).

2. Speed of the shot relative the jumper, as provided by upper body and arm
movement.

I suspect (but am not in anyway sure) that 1. will dominate in the rotation
technique, but that 2. will be larger for gliders.

(Possibly, some kind of comparison with a ``standing shot put'' might give
clues as to the true values.)

Again looking at energies, we get:

v^2 = 2as + K (where K is proportional to the constant work relating to 2.
above) and

v1/v2 = ((2as1 + K)/(2as2 + K))^1/2


Assuming, strictly for the sake of argument, a 50-50 distribution between 1.
and 2. for v2, we now have:

v1/v2 = ((s1/s2 + 1)/2)^1/2

and e.g. ((6/5 + 1)/2)^1/2 = 1.0488... or roughly half the increase of your
original calculations.

(A similar reasoning obviously applies to the discus.)

[eldrick]

i'm doubtful about relevance of 2

no matter if thrower is moving at 10m/s or 0m/s at release, it won't make his throwing arm intrinsically faster - the arm relative to body won't change speed

it's all due to increased speed relative to the ground with a bigger circle

[imaginative]

Actually, that is more or less the point: The speed increase due to a larger
circle will only affect 1, and any calculation that ignores 2. will provide too
large an improvement.

As for the relative size of 1. and 2.: By simply imagining an athlete making
a put from a stand-still, we have some clue that 2. has to be sizeable. How
sizeable, I do not know. Anyone with practical experience of putting normally
and from a stand-still?

[thorshammer]

Actually, that is more or less the point: The speed increase due to a larger
circle will only affect 1, and any calculation that ignores 2. will provide too
large an improvement.

As for the relative size of 1. and 2.: By simply imagining an athlete making
a put from a stand-still, we have some clue that 2. has to be sizeable. How
sizeable, I do not know. Anyone with practical experience of putting normally
and from a stand-still?

For most elite level giders, a 2m increase from a stand throw to a full glide is common. For spinners, it can be from 2-5m. Does that help?

[eldrick]

there may be something along the lines that a glider uses only linear increase in circle size, whereas a rotator uses the increased area of the circle more, a difference of a squared relationship

it's something to ponder...

[thorshammer]

there may be something along the lines that a glider uses only linear increase in circle size, whereas a rotator uses the increased area of the circle more, a difference of a squared relationship

it's something to ponder...

If you look at the length of the path that the shot travels in the spin and glide, the spin shot path is longer by a fair amount. Of course the longer implement path that the spinner has has to be offset by the fact that at some point the shot travels backwards. Perhaps something similar to the arc length formula from calculus (then take the result and divide over the time of the throw) could be used here?

[thorshammer]

Cantwell would very likely throw at least 1m farther with even 6" more to work with, which should let him drive to the middle more. So would have Oldfield. As for gliders, I would imagine that someone like Udo Beyer would have gotten some significant improvement with that kind of space.