Efficency of RCS angle

[Jestersage]

Recently, I was trying to do another mostly RCS build, and one thing I am curious about is the angle of the RCS thrusters. Specifically, perfect perpendicular vs 45 degree offset.

Aside from the typical "4 thrusters pointing outward along the 45 degrees line", I am also experimenting with a 45-degree rotated 4-RCS block. 

So I am not certain:

1) If the RCS block is rotated by 45 degree such that it forms an X, then it will be weaker in thrust. Unknowne effect on RCS DeltaV but I suspect it will be worse.

2) If the RCS block is not rotated, but at 45 degree X, it will be not at precise in compared to perpendicular layout.

Could someone confirm my observation? If so, is it because more RCS nozzle need to be used?

 

EDIT: So other people can see how bad cosine loss is: Say 0 is the direction you want, and 90 is the perpendicular

• cos 0 deg gives 100% thrust
• cos 90 deg gives 0 percent thrust
• cos 45 deg (4 way symtery) gives 70% each
• cos 60 deg (6 way symmtery, furthest away from the near 90 degree) gives 50%. Note that due to how symetry works, you will typically have 1 right on the 90 degree
• cos 30 deg (6 way symmtery, closest from the near 90 degree) gives 86.6%. 
• cos 22.5 deg (8 way symmetry further rotate offset, closest to 90 degree) gives 92%

Edited May 13, 2019 by Jestersage

[Aegolius13]

12 minutes ago, Jestersage said:

1) If the RCS block is rotated by 45 degree such that it forms an X, then it will be weaker in thrust. Unknowne effect on RCS DeltaV but I suspect it will be worse.

Yep, this is called a "cosine loss."  The amount of wasted thrust is proportional to the cosine of the inclination (0% wasted if the engine is pointing exactly where you want to go, 100% wasted at 90% inclination).  The effect on delta-v would be the same, since cosine losses decrease the amount of usable thrust generated per unit of fuel consumed.  It's akin to lowering the ISP of your thrusters.

The above should hold true for one-direction thrusters or regular engines.  I've never really delved into it with the multi-direction thruster blocks, but I think it would work the same way, since using the additional thrust directions (which are pointed even more in the wrong direction) would not be expected to improve efficiency. 

I'm not a MechJeb user, but I believe it provides some data on cosine losses. Don't know if this includes info from RCS, though.

(My very first post on this forum was on the same topic, so you're in good company!)

[Adenosine Triphospate]

3 hours ago, Aegolius13 said:

The amount of wasted thrust is proportional to the cosine of the inclination

I imagine this principle can be applied to all real life rocket engines. Even if the engine is perfectly aligned, not all the exhaust is ejected exactly parallel to the direction of motion. These deviations cancel each other out, so effectively delta-v is wasted.

[Jestersage]

11 hours ago, Aegolius13 said:

Yep, this is called a "cosine loss."  The amount of wasted thrust is proportional to the cosine of the inclination (0% wasted if the engine is pointing exactly where you want to go, 100% wasted at 90% inclination).  The effect on delta-v would be the same, since cosine losses decrease the amount of usable thrust generated per unit of fuel consumed.  It's akin to lowering the ISP of your thrusters.

Didn't even know about its actual existence (but I had a gut feeling) until today. Thanks.