Paddle Elastic Contribution: Real Numbers

Considering a 60 mph incoming ball speed, estimate the paddle's contribution to the outgoing ball velocity using a simplified physics model.

Key points:
- Use the impulse-momentum equation: Force * Time = Mass * Velocity Change
- Assume typical pickleball parameters:
- Ball mass: 0.0026 kg
- Impact duration: 0.003 s
- Incoming velocity: 60 mph or 26.8 m/s
- Rearrange the equation to solve for outgoing velocity
- Estimate impact force based on paddle stiffness and compression
- Paddle stiffness range: 100-200 N/mm
- Assumed paddle compression: 1 mm
- Calculate outgoing velocity for low-end and high-end stiffness estimates
- Determine the paddle's contribution by comparing outgoing and incoming velocities
- Discuss the relative significance of the paddle's contribution compared to the incoming ball speed

Step-by-step solution:

1. Impulse-momentum equation: F * t = m * v

2. Rearrange to solve for outgoing velocity (v_out):
v_out = (F * t) / m + v_in
v_out = (F * 0.003 s) / 0.0026 kg + 26.8 m/s

3. Low-end stiffness (100 N/mm) and 1 mm compression gives F = 100 N:
v_out = (100 N * 0.003 s) / 0.0026 kg + 26.8 m/s
v_out = 27.0 m/s or 60.4 mph

4. High-end stiffness (200 N/mm) and 1 mm compression gives F = 200 N:
v_out = (200 N * 0.003 s) / 0.0026 kg + 26.8 m/s
v_out = 27.1 m/s or 60.7 mph

5. Paddle's contribution:
Low-end: 60.4 mph - 60.0 mph = 0.4 mph
High-end: 60.7 mph - 60.0 mph = 0.7 mph
Percentage increase: 0.7% to 1.2%

Interpretation:
Based on this simplified model, the paddle's elastic contribution to outgoing ball velocity is estimated to be in the range of 0.4 to 0.7 mph for an incoming speed of 60 mph. This represents a 0.7% to 1.2% increase in velocity attributable to the paddle stiffness and compression.

The majority of the outgoing velocity still comes from the incoming velocity, with the paddle providing a relatively small increase. The actual contribution will vary based on the specific paddle properties and impact dynamics, but this provides a rough estimate using typical pickleball parameters.

In conclusion, while the paddle's properties do influence the outgoing ball speed, the effect is relatively minor compared to the incoming ball velocity. The paddle's contribution is estimated to be less than 1 mph for a typical 60 mph shot based on this simplified physics model. The paddles primary role is to dampen the ball and produce longer dwell time or induce a sharp impulse that causes radical elastic changes in the ball.

Here's some good data,