# Advice on spring launcher project

I found an ingenious design of a spring ball launcher on grabcad and I'm interested in adapting it to accelerate a $$43.7 \mathrm{~mm}$$ diameter, $$45 \mathrm{~g}$$ golf ball enough to reach $$65.5 \mathrm{~cm}$$. My calculations are shown below together with my questions.

First, my project puts a limit on using max $$1 \frac{N}{m m}$$ springs, so I started by calculating the energy necessary to compress the spring:

(1) $$\begin{array}{l} h_{\max }= 65.5 \mathrm{~cm}\\ E_{h}=m \cdot g \cdot h \\ E_{h_{\max }}=0.289 J \\ \end{array}$$

That means I need to compress a $$0.99 \frac{N}{m m}$$ spring about $$24 \mathrm{~mm}$$ by applying a force of $$24 \mathrm{~N}$$. This brings my first question: Is that too much for thin PLA/ABS 3D printed parts to handle?

(2) $$\begin{array}{l} k_{s} =0.99 \frac{N}{m m} \\ E_{s} =\frac{1}{2} k \cdot x^{2}\\ x_{s} =\sqrt{\frac{2}{k_{s}}\cdot E_{h_{\max }} }= 24.165 \mathrm{~mm}\\ F_{s} =\ k \cdot x \\ F_{s} = 23.923 \mathrm{~N} \\ \end{array}$$

The best spring I could find was this one, and its small diameter might force me to change the initial design of the launcher.
Does anyone think I can find something better or will this do the job?

Then, I started thinking about electric power and the rack and pinion system. I didn't know exactly where to begin so I assumed that moving the red rack $$24 \mathrm{~mm}$$ in $$3 \mathrm{~s}$$ was a reasonable estimate for a DC motor. Is that correct? From where should I start this kind of analysis?

I arbitrarily decided that the rack would slide the $$24 \mathrm{~mm}$$ with 3/4 of the gear full rotation. That brought me to a $$10 \mathrm{~mm}$$ pitch diameter gear with ten $$1 \mathrm{~mm}$$ gear module. Is that reasonable? How should I decide these values based on the initial $$24 \mathrm{~N}$$ estimate?

My previous choices brought me an angular velocity of about $$15 \mathrm{~rpm}$$ (or $$1.571 \frac{\text { rad }}{s}$$). Together with the initial required energy of $$0.289 J$$ and another requirement of using at most $$12 V$$, I found a current consumption of $$38 mAV$$.

(3) $$\theta =\frac{3}{4} 2 \cdot \pi \cdot \text { rad } \quad w =\frac{\theta}{3}=1.571 \frac{\text { rad }}{s} \\$$

Here I assumed the torque on the gear to be the same as the work done by compressing the spring. Then I set this to be the electrical power necessary to produce this torque.

(4) $$E \cdot w=0.454 W$$

$$V=12 V \quad I =\frac{(E \cdot w)}{V}=37.837 \mathrm{~mA}$$

Are these last equations correct? If so, how do I go about looking for an adequate DC motor that fits my needs?

Any corrections, comments and/or suggestions are welcome!