Saturday, March 04, 2006

 

Pace vs Bounce - 2

In the previous post, I talked about pitches with good pace but not bounce. I gave Sabina park as an example.While the shiny Sabina park pitch, beacuse of its lesser friction, offers pace, I dint explain why the 'bounce' of this pitch is not steep.

The Sabina park pitch is hard; this means its coefficient of restitution is high. Then why no steep bounce? Curiously the reason for this is beacuse of its pace! Lets see why...

First, what do we mean by bounce? It is the angle (with the horizonatal) with which the ball rises after it hits the ground. Greater the angle, steeper the bounce.

Now consider two pitches A and B. Both the pitches have identical values of coefficient of restitution.But pitch A is faster (has lesser friction) than pitch B. Now suppose a bowler bowls identical balls (around the good-length area) with the same speed on two pitches.

Pitch B being slower pitch, reduces the horizontal component with which the ball leaves pitch B, much more compared to pitch A. This causes the ball in pitch B to rise at a greater angle, compared to pitch A. The slower the pitch, the greater the angle with which it rises!!

Formally,
Uah = Horizontal component of velocity with which ball hits pitch A
Ubh = Horizontal component of velocity with which ball hits pitch B
Uan = Vertical (Normal) component of velocity with which ball hits pitch A
Ubn = Verical component of velocity with which ball hits pitch B

Uah = Ubh
------------------------------------------------(Since the deliveries are identical)
Uan = Ubn

The corresponding V values are the velocities with which ball leaves the pitch.

Vah = Horizontal component of velocity with which ball leaves pitch A
Vbh = Horizontal component of velocity with which ball leaves pitch B
Van = Vertical (Normal) component of velocity with which ball leaves pitch A
Vbn = Verical component of velocity with which ball leaves pitch B

Van = Vbn ----------------------------------(Since the restituitions for the pitch are identical)

But Vah > Vbh ----------------------------(Pitch A is faster than pitch B, hence the latter reduces the
horizonal component more)

(Tanof the) Angle with which ball rises on pitch A, Tan A = Van/ Vah
(Tan of the) Angle with which ball rises on pitch B, Tan B = Vbn/Vbh

Tan B > Tan A
==> B> A


Hence ball bounces more steeply in the slower pitch!

Consequences
  1. This means that sometimes (when the coefficient of restitution are the same) the faster pitch, has a less steeper bounce. (which is very non-intuitive).
  2. Then why is there good correlation observed between pace and bounce in pitches around the world.This is beacuse there is a good observed correlation between coeffcient of restitution and the lack of friction in the pitch.
  3. This explains why it is very awkward to play spin bowling in a tennis ball. Have you ever observed somebody driving "on the up" against slowly bowled tennis ball. I havent...People either go to the pitch of the ball or stay back and play against slow tennis ball bowling. This is because of the steep
    bounce at which the ball rises after it hits the ground. That is why this is called tennis-ball bounce.

Comments:
haiyoo! enna man idhu>?
 
Certain things are easier explained using notations; if you try to understand it, you will find it is as simple as 1+1=2.

But yeah, I am not sure if I will try to understand this, if it was written by somebody else :)
 
It was a tight fortnight work - Good to see so many posts to catch up with.

I am reminded of the advice given to Stephen Hawking by his publisher (of Brief History of Time): "For every equation you add, the number of readers would reduce by half."

Vijay, do be easy on us lay-people! :-) Having said that, I will read this as an intellectual exercise... er... soon.
 
Srikanth,

If you were me, you would have drawn some nice pictures to illustrate the point.

But unfortunately pictures are not my style. (read, "I suck in drawing")
 
(Suggested) correction: Vah = Vbh ----------------------------------(Since the restituitions for the pitch are identical)...should read Van = Vbn (typo, i mean).

Good un da Vijay. More such - particualry relevant to cricket - even if they might sound too obvious to u - still, do pen them da...wud be very informative and intresting to read.

ps - Hi Srikanth :).
 
Thanks again BK.
I really appreciate it.

I have updated.
 
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N. Vijayanand - ur comment here God & Music would be very much appreciated friend.

Thanx :)
 
by fsr the most thought provoking blog entry i have read in a long time...excellent!

but i have some questions on the previous post...will post them there ...on pace and bounce 1
 
MY GOD!!!
Thats atrociously sensational stuff!!
 
Thanks Girish!
 
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