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Most efficient speed/altitude for Whiplash Ramjet?


boriz
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Ok. My 'gut' was wrong. [email protected]/s gets you about twice as far as [email protected]/s.

The test:

A single whiplash engine with a single Mk1 liquid fuel fuselage holding 400 units of fuel and the minimum of aircraft around it.

Mechjeb2 autopilot did all the flying. I manually started the takeoff run, and once I was sure the aircraft was rolling straight, I engaged MJ. MJ did the rotation, climb, the entire flight. All flights were runway heading, 090.

I did four flights of different speeds (300m/s, 600m/s, 900m/s, 1200m/s), at each of six different altitudes (6km, 9km, 12km, 15km, 18km, 21km), for a total of twenty-four flights. 1200m/s was the limit for overheating. When the fuel ran out and the engine cut off, I immediately pressed F3 to record the range data.

After many hours, I learned four things. Firstly, as was said, the higher and faster, the better. Heat friction losses are negligible. Secondly, the heating effects are exactly the same for a particular speed, regardless of altitude. The 1200m/s run would always end with the Mk1 inline cockpit moments away from exploding (full heat bar). Thirdly, I should have used bigger wings. I repeated the last (highest and fastest) run with the same aircraft, but twice the wing area, and got a significant range improvement because of the lower AoA. But this is just supposed to be a test of the engine.

And lastly, perhaps most surprisingly (for me), 400 units of fuel and one Whiplash is more than enough to circumnavigate Kerbin along its equator and land back at the KSC with fuel to spare. Who'd have thunk it?

The 18km and 21km data is missing a 300m/s run because the autopilot couldn't cope with the extreme angle of attack required when going so slow in such thin air. I spent ages trying to tune the PID but eventually gave up.

The results:

Horizontal scale is Range in Kilometres. Vertical scale is altitude subdivided into speeds. The duration of each flight was also recorded, but omitted on the chart, since it can be easily calculated.

chart.png

The testbed:

screenshot455.jpg

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Once supersonic, lift to drag ratio stays fairly constant, only dropping maybe 10-20% from Mach 2.5 to Mach 5.  You cover twice as much ground per second, at only slightly higher fuel cost.  In addition, the closer you get to orbital speed, the less you feel the effects of gravity, and the higher you are, the weaker gravity is.  Together, this means going as fast as you can, as high as is reasonable, reduces the amount of lift you need to have to continue flying.  Since lift to drag ratio is relatively constant, this means less drag as well.

End result being that with whiplashes or rapier engines, the most efficient speed and altitude is as fast as you can as high as you can.

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3 hours ago, boriz said:

By efficient I mean greatest distance covered for least fuel used.

The efficiency in terms of thrust per fuel-burn (the ISP) is constant for KSP engines (wiki link).  I suppose the idea is that when the ramjet catches more air, proportionally more fuel is burned.  So that means you are looking for the conditions to give you the best speed per thrust, which in cruise is the same as speed per drag.

The attitude (pitch) for lowest drag in level flight is called the best-L/D angle (best lift / drag).  This angle of attack also gives you the best glide ratio, so you can find it experimentally by finding the pitch that lets you glide the furthest with engines off.  For typical KSP aircraft this attitude has the nose pointing near the top of the prograde  :prograde: marker. 

At low altitudes, the best-L/D speed is pretty slow.  At higher altitudes, the best L/D angle  relative to prograde stays fairly constant until you near the speed of sound, at which point you need to point a bit closer to prograde to reduce the extra parasitic drag (as modelled by KSP).

Then to make drag as low as possible to climb as high as you can to the thinner air, until you find you need to pitch up further than best L/D angle just to stay aloft.  If That generally means to fly near the ceiling altitude of the aircraft, full throttle.   A good fuel-per-distance design would have enough wing area that you are below the speed of sound in this configuration, to avoid the extra drag at and above the speed of sound.

There have been some fuel-efficiency challenges (link link link) but none I can see specific to the Whiplash engine.

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LD max will yield good flight time, but will not give you good range.

Best range will nearly always be considerably faster than LD max.  There is no secret formula for best range speed.  It’s ‘Whatever speed gives you the most distance covered per unit of fuel.’  Really the only way to effectively determine that speed is through flight testing.

One factor that will affect best range speed is obviously the engine.  The airplane design plays a big part too though.  So what works for one design with the Whiplash might not be the best solution for a different plane using the Whiplash.

As @Lt_Duckweed said,  in general the higher and faster you go, the better your range will be with the Whiplash and Rapier, probably the Panther too.  

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Posted (edited)

Thanks guys. The twin engine plane in the picture in my OP, is my 'fast recon', and can easily go fast enough to melt. My 'gut' speed of 900m/s is because beyond that, I get some serious heating effects. This implies a lot of energy lost to drag, but I don't know how KSP models that.

I've built a small test plane to do some experiments at various speeds and altitudes. Using MJ autopilot for consistency. Assuming I don't get bored, I'll post my results here.

BTW. I never use the Rapier. I feel it's 'cheating' to use future tech.

My testbed:

screenshot443-Medium.png

Edited by boriz
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43 minutes ago, boriz said:

The results:

Thank you for doing this. Much of this I already 'knew' from my own planes and testing, but it always helps to see it confirmed with actual data. Much appreciated, also with the very readable presentation.

One tip that may open a world for you in matters of fuel efficiency: add a few degrees of Angle of Incidence to your wings (rotating them so the leading edge is pointing a bit upwards compared to the trailing edge). This allows for lift to be generated while keeping the main body of the plane as close to prograde as possible, which minimizes body drag. Conversely it may allow smaller wing area to maintain the same lift, which would also lower total drag. both of those tend to translate to more fuel efficient flight, combined with the more common optimizations.

 

45 minutes ago, boriz said:

400 units of fuel and one Whiplash is more than enough to circumnavigate Kerbin along its equator and land back at the KSC with fuel to spare. Who'd have thunk it?

Get accustomed to tuning your plane designs to efficient flying, and you'll notice it's possible to do much better even, with smaller/slower engines too.

How about on a single Juno, using less than 86 units of LF?  Flying at mach 2+ and relatively high was definitely key for this one too.

 

I'll be interested to see what designs you come up with. Do share!

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Instead of mechjeb trying to maintain a certain speed and altitude, it's probably best to just punch the throttle to max and leave it there for the duration. This ensures that you're as close as possible to the far right end of the engine's mach curve, so you get the most speed for the least thrust. Also you'll fly higher which translates to lower thrust.

Actually, this isn't quite true. On my jet engine endurance mission, I ended up flying so high that the Rapier started to flame out at full throttle, so I had to throttle back. This still led to improved efficiency however, as I could still operate at the Rapier's limit. However, one possible improvement would be to have wings in cargo bays, so I could take off and then reduce lift for cruising.

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