Is recoil weight any good?

[Patrik]

I have understood that the general consensus it that recoil weight is a measure of how hard, for a given head speed, the racquet hits the ball, it is even also referred to as "hitting weight".
I asked ChatGPT, "In tennis, what effect does people think "recoil weight" has?" As ChatGPT is trained on the text of the internet it would summarize what people actually write on the internet. The answer was:

Here are some effects that people believe recoil weight has:

• Power and Plow Through:
  • Higher Recoil Weight: Racquets with higher recoil weight often provide more "plow through," meaning the racquet can drive through the ball more effectively. This can result in more powerful shots as the racquet's momentum helps to propel the ball forward.
  • Lower Recoil Weight: A lower recoil weight might reduce the power of shots since there is less mass behind the ball at the moment of impact.

I did the calculations to see if this is true. I chose two racquets from this source: https://docs.google.com/spreadsheets/d/1Esa_cqL8wbAv0J1GGq-t7N_yoqKOdCPpbIwODjdqgWE/edit?gid=0#gid=0
sorted it by swing weight and chose Kyrgios and Lazarov as they had similar swing weight but very different recoil weight. For the same swing speed the higher recoil weight racquet should then produce a higher ball speed, right?

Here is a link to an Imgur post showing the graph of the results:

https://imgur.com/a/r2DG4P8

There is also a schematic of the calculated scenario and the derivation of the formula used to calculate the ball speed after the impact. Hover the image and click the right and left arrows to see the other images.

Here is a summary of the input data used: ( See the second picture of the Imgur post for an explanation of what the values represent. )
% SI-units.
e = .8; % Coefficient of restitution.
rh = .1; % Instantaneous swing center from butt cap, meters.
wi = 30; % Initial angular velocity around the instantaneous center, radians per second.
vb1 = -10; % Initial ball velocity, m/s. Negative because moving towards the racquet.
mb = .058; % Mass of the ball.
rs = linspace( .4, .6, 100 ); % Distance to ball strike from the butt cap.

% Lazarov's racquet data. Swing weight = 323.2 kgcm^2.
m = .3201; % mass
rcg = .3491; % Distance to balance point ( center of gravity, cg ).
Icg = .01206; % Recoil weight, kgm^2.

% Kyrgios' racquet data. Swing weight = 325 kgcm^2.
m = .34;
rcg = .312;
Icg = .01686;

 

[aaron_h27]

Average recoil weight on ATP Tour - 176

Average recoil weight on WTA - 164

Do what you want with that information.

 

[zoingy]

I have understood that the general consensus it that recoil weight is a measure of how hard, for a given head speed, the racquet hits the ball, it is even also referred to as "hitting weight".

Recoil weight is the moment of inertia around the racquet center of mass, but I don't think there's a direct reason why the center of mass is the point that's relevant per se. I think the more direct measure of how hard a racquet (or rather, a rod, as we're assuming in these models) hits the ball relative to speed, point of contact, and mass distribution may be effective mass. It's the mass of a point mass that would cause an equivalent collision effect as colliding with the rod at some point offset from the rod's com.

A higher recoil weight causes effective mass to not fall as sharply when colliding farther away from the balance point, which matches up with the shape of the curves that you calculated.

I haven't dug into the details yet, but I wonder if there's an intuition behind why your model shows Lazarov's racquet to have a higher peak exit velocity, at a point closer to the buttcap. To me that sounds counterintuitive given it's lower mass and higher balance point.

Interesting stuff!

 

[Patrik]

@zoingy, I did the math to not have to intuit, and to show that what people intuit is wrong. I must have intuited that Lazarov would likely have a higher peak velocity or I would not have put in the work.

 

[Donmikan]

I have understood that the general consensus it that recoil weight is a measure of how hard, for a given head speed, the racquet hits the ball, it is even also referred to as "hitting weight".
I asked ChatGPT, "In tennis, what effect does people think "recoil weight" has?" As ChatGPT is trained on the text of the internet it would summarize what people actually write on the internet. The answer was:

Here are some effects that people believe recoil weight has:

• Power and Plow Through:
  • Higher Recoil Weight: Racquets with higher recoil weight often provide more "plow through," meaning the racquet can drive through the ball more effectively. This can result in more powerful shots as the racquet's momentum helps to propel the ball forward.
  • Lower Recoil Weight: A lower recoil weight might reduce the power of shots since there is less mass behind the ball at the moment of impact.

I did the calculations to see if this is true. I chose two racquets from this source: https://docs.google.com/spreadsheets/d/1Esa_cqL8wbAv0J1GGq-t7N_yoqKOdCPpbIwODjdqgWE/edit?gid=0#gid=0
sorted it by swing weight and chose Kyrgios and Lazarov as they had similar swing weight but very different recoil weight. For the same swing speed the higher recoil weight racquet should then produce a higher ball speed, right?

Here is a link to an Imgur post showing the graph of the results:

https://imgur.com/a/xEDzYt7

There is also a schematic of the calculated scenario and the derivation of the formula used to calculate the ball speed after the impact. Hover the image and click the right and left arrows to see the other images.

Here is a summary of the input data used: ( See the second picture of the Imgur post for an explanation of what the values represent. )
% SI-units.
e = .8; % Coefficient of restitution.
rh = .1; % Instantaneous swing center from butt cap, meters.
wi = 30; % Initial angular velocity around the instantaneous center, radians per second.
vb1 = -10; % Initial ball velocity, m/s. Negative because moving towards the racquet.
mb = .058; % Mass of the ball.
rs = linspace( .4, .6, 100 ); % Distance to ball strike from the butt cap.

% Lazarov's racquet data. Swing weight = 323.2 kgcm^2.
m = .3201; % mass
rcg = .3491; % Distance to balance point ( center of gravity, cg ).
Icg = .01206; % Recoil weight, kgm^2.

% Kyrgios' racquet data. Swing weight = 325 kgcm^2.
m = .34;
rcg = .312;
Icg = .01686;

Its very interesting that the curves peak at different points. Im interested in finding out how to setup a racket so that the max speed happens in the middle of the stringbed, around 52cm.

 

[Patrik]

Its very interesting that the curves peak at different points. Im interested in finding out how to setup a racket so that the max speed happens in the middle of the stringbed, around 52cm.

The position of the sweet spot moves closer to the CG when hitting balls coming fast and moves farther out for a "snappier" swing. It will not always stay at 52 cm.

 

[Donmikan]

I have understood that the general consensus it that recoil weight is a measure of how hard, for a given head speed, the racquet hits the ball, it is even also referred to as "hitting weight".
I asked ChatGPT, "In tennis, what effect does people think "recoil weight" has?" As ChatGPT is trained on the text of the internet it would summarize what people actually write on the internet. The answer was:

Here are some effects that people believe recoil weight has:

• Power and Plow Through:
  • Higher Recoil Weight: Racquets with higher recoil weight often provide more "plow through," meaning the racquet can drive through the ball more effectively. This can result in more powerful shots as the racquet's momentum helps to propel the ball forward.
  • Lower Recoil Weight: A lower recoil weight might reduce the power of shots since there is less mass behind the ball at the moment of impact.

I did the calculations to see if this is true. I chose two racquets from this source: https://docs.google.com/spreadsheets/d/1Esa_cqL8wbAv0J1GGq-t7N_yoqKOdCPpbIwODjdqgWE/edit?gid=0#gid=0
sorted it by swing weight and chose Kyrgios and Lazarov as they had similar swing weight but very different recoil weight. For the same swing speed the higher recoil weight racquet should then produce a higher ball speed, right?

Here is a link to an Imgur post showing the graph of the results:

https://imgur.com/a/xEDzYt7

There is also a schematic of the calculated scenario and the derivation of the formula used to calculate the ball speed after the impact. Hover the image and click the right and left arrows to see the other images.

Here is a summary of the input data used: ( See the second picture of the Imgur post for an explanation of what the values represent. )
% SI-units.
e = .8; % Coefficient of restitution.
rh = .1; % Instantaneous swing center from butt cap, meters.
wi = 30; % Initial angular velocity around the instantaneous center, radians per second.
vb1 = -10; % Initial ball velocity, m/s. Negative because moving towards the racquet.
mb = .058; % Mass of the ball.
rs = linspace( .4, .6, 100 ); % Distance to ball strike from the butt cap.

% Lazarov's racquet data. Swing weight = 323.2 kgcm^2.
m = .3201; % mass
rcg = .3491; % Distance to balance point ( center of gravity, cg ).
Icg = .01206; % Recoil weight, kgm^2.

% Kyrgios' racquet data. Swing weight = 325 kgcm^2.
m = .34;
rcg = .312;
Icg = .01686;

Could you please link the graph, i would like to tinker with the values a bit, and it would be usefull to see values on the x axis up to 65.

 

[Tranqville]

There is a search function in this forum, do use it:

Who Cares about Recoil Weight?

Advanced players care about recoil, and here’s why. Swingweight, twist weight, and recoil weight (also called ‘hitting weight’) all measure the inertia of a racquet along different axes or planes. Recoil weight shares the same plane as swingweight but its axis is the balance point (vs. the...

tt.tennis-warehouse.com

 

[Patrik]

There is a search function in this forum, do use it:

Thank you for your valuable contribution to this thread.

 

[Patrik]

Could you please link the graph, i would like to tinker with the values a bit, and it would be usefull to see values on the x axis up to 65.

I appreciate your enthusiasm, I will provide the code but first you should know that this simulation models the racquet as infinitely stiff. Therefore the simulation is not to be used as a quantitative measure but rather as an indication of the relative qualities between two racquets. Secondly it currently models the coefficient of restitution as a constant, you could fairly easily make it a function of rs. Make sure you understand the limitations of the model.

To tinker with this model download octave

Download

GNU Octave is a programming language for scientific computing.

octave.org

and run this code:

% Tennis racquet simulation.
% Note, the racquet is simulated as infinitely stiff and the coefficient of restitution as a constant.
% Therefore the simulation is not to be used as a quantitative measure but as an indication of relative qualities between two racquets.
% Make sure you understand the limitations of the simulation before you cut the beam.
% At some point in time there was a schematics picture and derivation of the formula here: imgur.com/a/r2DG4P8
% Author Patrik Tegelberg. All rights reserved.

clear
clf

% SI-units.
e = .8; % Coefficient of restitution.
rh = .1; % Instantaneous swing center from butt cap, meters.
wi = 30; % Initial angular velocity around the instantaneous center, radians per second.
vb1 = -10; % Initial ball velocity, m/s. Negative because moving towards the racquet.
mb = .058; % Mass of the ball.
rs = linspace( .4, .6, 100 ); % Distance to ball strike from the butt cap.

% Lazarov's racquet data. Swing weight = 323.2 kgcm^2.
m = .3201; % mass
rcg = .3491; % Distance to balance point ( center of gravity, cg ).
Icg = .01206; % Recoil weight, kgm^2.
vb2 = ( mb * vb1 * ( rs - rcg ).^2 + Icg * ( ( mb / m - e ) * vb1 + wi * ( 1 + e ) * ( rs + rh ) ) ) ./ ( ( 1 + mb / m ) * Icg + mb * ( rs - rcg ).^2 );
plot( rs, vb2 )
hold on
grid on

% Kyrgios' racquet data. Swing weight = 325 kgcm^2.
m = .34;
rcg = .312;
Icg = .01686;
vb2 = ( mb * vb1 * ( rs - rcg ).^2 + Icg * ( ( mb / m - e ) * vb1 + wi * ( 1 + e ) * ( rs + rh ) ) ) ./ ( ( 1 + mb / m ) * Icg + mb * ( rs - rcg ).^2 );
plot( rs, vb2 )

hxl = xlabel( "rs, Distance to ball strike from butt cap [m]" );
hyl = ylabel("vb2, Ball velocity [m/s]" );
hLegend = legend( 'Lazarov, Recoil weight = 120,6','Kyrgios, Recoil weight = 168,6', 'Location', 'southwest' );
set(hLegend, 'FontSize', 14)

 

[Donmikan]

Thanks a lot! Yes, i was interested in just comparing between setups. I want to see what happens at even higher values of x.