Angled rockets

[mariohobbs]

Many large kiloton launchers I’ve seen tend to angle their rockets, is that good because to me it seems like half the thrust of the rocket would be lost if the engine pointed 45* is that true or is there something im missing?

 

[DioSpaghetti]

I think it's just a cooler way to get around engine heating, and yes you lose thrust

 

[Altaïr]

You lose thrust, but not as much as you probably expect. When an engine is turned by an angle α, its vertical thrust is equal to total thrust multiplied by cos(α). For small values of α, cos(α) is close to 1, so the losses are not much. You can notice it with the Taylor approximation for small angles:
cos(α) = 1 - α²/2
α must be expressed in radians (1 rad ≈ 57.3°)

Take this cool and beautiful launcher for example:

The engines are angled by 15°, and cos(15°) is approximately equal to... 0.966. So in the end, the loss is about 3.4% only

If you angle them by 45°, the loss would be much more noticeable though, at 29.3%

 

[Axiom]

Many large kiloton launchers I’ve seen tend to angle their rockets, is that good because to me it seems like half the thrust of the rocket would be lost if the engine pointed 45* is that true or is there something im missing?

As the person who made (probably) the largest rocket with angled engines, you don't lose as much thrust as you would expect
If they were angled by 10 degrees, you only lose 1.5% of your thrust, which is quite minimal. It's also not too difficult to get them to be angled at 10 degrees.

You can see it on my kiloton launcher Ragnarok

With the combination of slaced and angled engines, I can achieve an average engine angle of less than 10 degrees, which results in very neglibile losses