Smooth and square

Smooth and square

Since the dawn of rocketry, almost all rockets have had a round cross section, but is this always the best solution?

There are good theoretical reasons to use a round cross section for a rocket body:

  • It is an efficient shape for a pressure vessel.
  • It has the minimum circumference to cross section area.
  • It is relatively easy to build from rolled and welded sheet metal.

However a rocket is not all propellant tanks, but also require a lot of practical “details” like a nosecone, a payload section, propellant feed lines, electrical wiring etc.

Additionally it is easy to forget in todays 3D printer craze that most materials are particularly practical and economical to work with in certain shapes and forms.

Many practical materials are available in sheet form, in particular sheet metal and plywood. The big advantage of using these materials is that they are readily available as semifinished products. Compared to moulded composites there is no need to produce molds before building a part, instead you simply cut the required panels out of a sheet and join the panels together to form a 3D shape.

An important characteristic of sheet materials is that they are relatively easy to bend in one, but not two directions at once. Mathematically they are limited to single curvature surfaces, maybe with a little bit of double curvature if forced.

When used in a pressure vessel, sheet material is often used to produce the cylindrical part of the vessel with a round cross section. But if this route is taken for a rocket body, problems are encountered when trying to make a nosecone. It is virtually impossible to make a longitudinal smooth round shape of sheet material, without restorting to cutting the material into multiple smaller pieces and trying to join them accurately together again.

What would happen if we do not need a round rocket cross section?

If we make the rocket body with sheet material without transversal curvature, we could readily bend the material into any curvature in the longitudinal direction. Thus the lack of transversal curvature opens the possibility of a completely smooth longitudinal body shape with a minimum number of parts and joints.

What cross section should we use?

We obviosly need to have stuff inside the rocket body; mainly propellants, propulsion systems, feed lines, recovery systems and payload. A triangular cross section is a possible solution with the least amount of panels, but why not use one more panel and make it a square cross section?

Squaring the circle

In a pressure fed rocket, we want the actual propellant tanks to be round cylinders for structural reasons.

However in order to reduce the drag, particular at transonic and supersonic speeds, it is important to keep the crossection area to a minimum for a given propellant volume. See Whitecomb area rule and Sears-Hack body for details.

In a given rocket length, this means maximising the effective propellant tank crossection area to rocket body crossection area. For a quick analysis we can imagine that we have propellant tanks of diameter D = 1, if we place 4 tanks in parallel in a rectangular grid configuration we get an effective propellant tank crossection area of 4(π/4)D^2 = π. A close fitting rectangular rocket body will have a side length of 2D = 2 and thus a crossection area of D^4 = 4. Thus we are utilizing π/4 = 78.5 % of the body crossection area for propellent tanks.

Smooth and square

In reality of course, the skin thickness of the rocket body lowers the practical ratio a bit. But for now lets compare this efficiency with another “packing method”. Packing 7 round cylinders into one larger round cylinder seems efficient, the outer 6 cylinders exactly touch both the central cylinder and each other.

Disk pack7.svg
By Koko90 - Own work, CC BY-SA 3.0, Link

The 7 cylinders of diameter D = 1 can be packed into an outer cylinder of diameter 3D. The combined crossection areas of the 7 smaller cylinders is 7(π/4)D^2 = 7pi/4, while the enclosing cylinder has a crossection area of (π/4)(3D)^2 = 9π/4. This means that 7/9 = 77.8 % of the body crossection area is utilized for propellant tanks. Based on crossection area utilization, the square crossectioned rocket body is actually more efficient then the 7 in 1 cylinder packing method.

Touch wood

The main rational for using a non round crossection is ease of manufacturing by using sheet material. But what sheet material is suitable?

Here we may take some inspiration from a completely different kind of vehicle, something designed for floating in water: Link

This vehicle defies the usual notions of a wooden boat: Heavy, slow, constructed of thick timber etc. Instead its a surprisingly light weight monoque structure of marine plywood, being ligther then a comparable glasfiber kayak.

A mini space shot ?

Combining the above design elements with the self pressurizing N2O/IPA propulsion system from Liquid Draupner we have the potentiel to create a small vehicle combining efficient aerodynamics, relatively high mass ratio and optimized long burning time.

A recipe for a mini space shot?