What is the required torque for a servo to swing a 5lb golf club at 120 MPH?

[GolfRobots]

Homework Statement

I am building a servo, to hold a golf club, and hit golf balls. My problem is, I do not know how powerful of a servo is required to swing the weight of the club/apparatus.

Homework Equations

The arm of that holds the club, including the club, is 5 lbs. Most of the weight is within 1' of the servo shaft. The golf club + the arm is 55" long. In order for the club to move from 0 to 120 MPH within 180 degrees rotation, how powerful of a servo would I require? How much torque would be required to move that weight to accelerate the end of the club, which is 55" away, to 120 MPH?

The Attempt at a Solution

I assume that the shaft would need to accelerate about 1/55 of 120 MPH, or about ~2.2 MPH. So a the servo would have to rotate the shaft about 2.2 MPH starting at 0 MPH to get to 2.2 MPH by 180 degrees, or half rotation.

How much torque is required to do that? I thank you for your support and help, in advance. I am building this robot servo to hit golf balls to create a hobby my son and I can do and learn from together. he is 14. Since he is maybe going into mechanical engineering, this will give him good experience to build off.

 

[jedishrfu]

Why golf balls? why not tennis balls? It seems that this would be quite dangerous if it hit someone or broke apart and tossed the club somewhere.

Here's an example of a Robot golf ball tester:



and here's Rory vs the robot:

 

[CWatters]

The starting point is the equation..

Torque = Moment of Inertia * angular acceleration

You will need to estimate the moment of inertia of the combined servo rotor, arm, club etc. Perhaps break the system down into regular shapes (eg a cylindrical rod to model the club shaft) and look up equations for the moment of inertia (eg for a rod rotated about one end). Then add up all the individual moments of inertia to get one combined value for the composite.

I believe the angular acceleration can be calculated using..

v² = u² + 2as

where

v = the final angular velocity (rads/s)
u = initial angular velocity (probably zero)
a = the acceleration in rad/s^-2
s = the angular displacement (rads) over which the acceleration occurs.

solve for a the angular acceleration.

In addition to the torque required to accelerate the servo rotor and club you might need to add an allowance for air resistance. You might need help from an aerodynamics expert to estimate the aerodynamic drag force on the club head at max velocity and then multiply that by the length of the club to get a rough idea of the torque required to overcome air resistance.

I would also consider adding an additional safety factor as the above calculations are only going to give you estimates.

 

[CWatters]

Google found this article...
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3899668/

In it table details the work done (energy expended) by 4 golfers striking a ball. It varies from about 900 to 1500 Nm

You could use this to estimate the torque required ...

Work = Torque * Angular displacement.
or
Torque = Work/Angular displacement

Lets say

The angular displacement while accelerating the club is 180 degrees (= 3.14 rads) and the work is 1500Nm = 1500 Joules then the required torque is around

1500/3.14 = 480 Nm

 

[GolfRobots]

480 Nm was double what I thought it would take. That is very helpful as an estimate. Thank you. I will seek to make the arm "longer" and the overall weight of the arm+club, under 4 lbs and try and save weight, so I need less Nm.

I like the idea of golf balls, because I believe a lot more can be learned from golf balls, and also, golf balls are much more interesting. I have a complete net enclosure, so its as close to safe as it gets.

Thank you for all your replies, I greatly appreciate your kindness.