What is the minimum size of a ramjet?

Question

Having recently learned that 155 mm ramjet artillery shells are now a thing, I wonder how much ramjet engines can be miniaturized. Could we see ramjet tank shells? Man-portable recoilless guns? Shotgun shells? Rifle bullets? For less martial applications, could we see micro-ramjet engines for small drones, similarly to micro-jet engines? (Whether or not it would actually sell if built is out of the scope of the question, let's simply imagine that there is a market for ramjet-powered microdrones.)

Given current (or near-future) manufacturing techniques, what would be the limiting factor for ramjet miniaturization? What would be the performances for the smallest engines, and how difficult/expensive would it be to make them? Are there theoretical physical limits to the minimal size of a ramjet engine?

Note: this ramjet-assisted shell is probably using solid fuel, but limitations for liquid fueled ramjet specifically are also relevant.

Answer 1

Ramjets could be miniaturized, but at some point, air viscosity and boundary layer thickness will make it impossible for them to work. Simply put, the intake hole will get so small that air will find it easier to flow around the whole thing and ignore all of its complicated inner structure.

In more technical terms, as the intake shrinks, intake velocity will approach an asymptotic limit regardless of flight velocity due to boundary layer friction, and for very small intakes, the air mass flow will be insufficient to sustain fuel combustion. That point seems to be somewhere in the centimeter range, but an engine becomes increasingly less useful as it approaches this point. Manufacturing parts this size isn't a problem even now.

Ramjet shells can help long-range artillery, but ramjet tank shells would not be effective in combat.

The figure of merit for tank rounds is their high-density penetrator's sectional energy at the target. Discarded sabot rounds are more effective at delivering this than any kind of engine internal to the projectile. Combat ranges are short enough to preserve the velocity.

If you had to use some sort of engine for a tank projectile, it would be a rocket. The reason is easiest to explain in numbers. At a range of 7.5 km with average 1.5 km/s velocity and a 10 kg round, to get 500 m/s of delta-V, you need 10 g = 1 kN of thrust (engine), plus 50 seconds of impulse (fuel). We'll ignore engine mass for the first approximation.

A rocket with TWR=50 and ISP=250 seconds will weigh 100 kg / 50 = 2 kg for the engine + 10 kg * 50/250 = 2 kg for the fuel, for 4 kg total.
A ramjet with TWR=5 and ISP=1000 seconds will weigh 100/5 = 20 kg for the engine + 10 kg * 50/1000 = 0.5 kg for the fuel, for 20.5 kg total.

Simply put, when flight time is this short, a heavy engine like a ramjet doesn't pay for the minute amount of fuel (or rather oxidizer) mass it saves vs a light and powerful rocket.

This applies to all combat applications within visual range: rockets are better, and guns are better still if you can afford the launcher weight. Beyond visual range, rockets or hybrid gun/rockets take over, and past 100 miles, air-breathing engines become viable.

Answer 2

Back in the 1980's I saw a small ram jet from the 1950's to be used in model boats, planes and cars. (1.25-2" diameter and 16-20" length.) The accompanying literature suggested using a baby food jar as a fuel tank. It used gasoline. I expect anything today would utilize a bit more sophisticated (and safer) positive control of the fuel. It was considered at that time to be the most powerful jet engine with the highest weight to thrust ratio in the world. It was very light weight since it was essentially an empty tube with a small compression head. Ramjets, despite some of their shortcomings, appear to be an economical alternative to complex turbine engines. The MIG-21 was an awesome aircraft which was essentially an engine with a seat strapped to it.

I think it would be fairly easy for someone with a few engineering tools to make a small ramjet. Expect to use double hearing and eye protection and devote a lot of fine tuning time as it will likely be a labor of love. Your neighbors will not like it.

Answer 3

Well, physical lab-size prototypes, based upon a variety of factors, would suggest 40mm, perhaps 18.5mm (12 gauge) as a practical testbed minimum bore diameter. There has also been some 50/12.7mm work, perhaps smaller if the gyrojet is considered. Theoretical limits are speculative, because designs would vary. There are atom stacked electric motors. External projectile scram power presents itself as a variation on a theme for smaller bore projectiles, using the projectile itself as the solid fuel. Like a self destruct mechanism, it dissolves down range. Powered vehicles get into the size/payload/altitude/range issue very quickly, along with acceleration and thermal survival of payload at ram/scram velocities. 50 year time-frame? Centimeters and grams. 22nd century? Molecular. Best guess.