## Thursday, April 19, 2012

### 3D Printed Rockets: The Cost Curve

If you've been around the rocket community, you may have heard of the "square cube law".  Basically, there are some physical parameters of machines that vary as a function of the square of length dimensions.   Thrust in a rocket engine for instance, is a function of the throat area, which is in turn a function of the throat diameter squared.   Volume and therefore mass is a function of the cube of a length parameter.   As a result, when scaling up the thrust of a rocket engine, the mass only increases with the square root of the ratio of the thrust.

So what?  In manufacturing, part of the cost of making a part is the amortization of the capital cost of the machine used to make a part.  In conventional machining techniques, labor and other costs also play heavily. However, in additive techniques like DMLS, the cost to make a part is largely driven by the cost of the DMLS machine:  as a result, the cost of a part is generally proportional to the volume of metal in the part.

Consider the three chamber designs above.   The chambers progress up in thrust by a factor of 10 from right to left.   So the first chamber is 10 lbf thrust, the second 100 lbf, and the third 1000 lbf.   Because of "the square cube law" the chamber on the right only has about 10 times as much metal material as the chamber on the far left - despite having 100 times the thrust.   Do to the wonder additive manufacturing, we could estimate that if the 10 lbf chamber cost \$1, then the cost of the 1000 lbf chamber would only be about \$10. In real numbers, that means a 1000 lb chamber could probably be printed using DMLS for less than \$10,000 - a pretty significant price point compared to other manufacturing techniques.

I recently got an email from someone asking about the feasibility of a 50lbf version of my DMLS chamber.  I spent a few hours and drew the above model.   Interestingly, this model has nearly the same metal material as Version1 of my DMLS chamber - which means that despite being rated for 5x the thrust, it could be made for roughly 1.5x the cost.   The primary mass reduction comes from the learning curve of the first DMLS chamber and being able to downsize based on the test results from V1.