This memo about weathercocking relates specifically to the UBC rocket sonde project described in "Water Waiver". Some of you hobby rocketeers might be able to apply some of the concepts in your rocketry:
In the process of thinking through the tandem engine concept, I have spent a lot of time understanding the dynamics of weathercocking. At first, I accepted Mike's explanation about the rocket only weathercocking during the engine burn... which is true... But there is a bit more to it. I'm glad it is windy at my launch pad, because it forces me to deal with it. The other statement that is only sort of marginally true is that the safety factor space between the CP and CG effects weathercocking.
First Mike's statement. If you picture the rocket fired vertically from a cannon in a strong wind with no engine burn... The momentum of the rocket is vertical... so it will try to continue on that path. But the rocket with its fins, like the tail feathers of an arrow will always weathervane (point at the relative wind)... which is not the same as weathercocking (going up wind). The rocket will always point directly into the relative wind. When the rocket is going extremely fast, the relative wind is very vertical, so the rocket will point virtually straight with its track. As the rocket slows, even though it might still be moving directly vertically, it will gradually point farther and farther horizontal into the wind. When the rocket reaches apogee, it will be horizontal, pointed directly into the wind... even though its path has not strayed from a vertical line. (The wind should theoretically, gradually accellerate the rocket down wind, until it has a horizontal component equal to the wind speed. So even though the rocket weathervanes into the wind, its path is curved slightly down wind.)
Now picture the rocket under power in the first couple seconds of flight. Since the direction the rocket will point, is the hypotenuse of the vertical speed of the rocket, and the horizontal wind speed... the rocket will tend to weathervane the farthest off vertical when it is going the slowest... which is just after it leaves the launch tube. During this first fraction of a second of flight, the rocket is pointed off vertical... so the thrust of the engine is off vertical, and that begins to accellerate the rocket horizontally into the wind... weathercocking. As the speed quickly rises, the rocket quickly points more directly along its new path... so the thrust is now in line with the path. So the rocket will follow the new path in a relatively straight line... which is just what you see at the rocket meets.
This fits well with what Mike was saying about our needing to use a very high thrust engine. We want to minimize the time that the rocket is going relatively slowly in the first fraction of a second of flight. The longer the launch tube, the more vertical it will go in a strong wind as well.
Now to the other statement about the CG to CP spacing. The above weathervaning will occur no matter what the CG to CP spacing is. So the only effect it has is: A rocket that is barely stable might weathervane a tiny bit slower. Since the rocket has some yaw inertia, its weathervaning will lag slightly, as it begins to weathervane from its vertical allignment in the launch tube. This lagging will occur most, just as the rocket is leaving the launch tube. So this lagging does decrease weathercocking . Making the rocket longer would help, because it would have more yaw inertia. The effect of changing the CG to CP spacing is only slight, however. There are other effects regarding the CG to CP spacing that have a much greater effect... like safety, weight, and drag. A rocket that is marginally stable might be more likely to oscillate/wobble in the first second of flight. When the rocket does overcome its stationary yaw inertia, the rocket will yaw into the wind... but now the rocket's moving yaw momentum will tend to continue past its proper weathervane headding.
Applying all this to the tandem engine concept. It is crucial that the rocket accellerate real hard in the first second of flight. The first engine would need enough thrust to accellerate the rocket right at the structural G limit of the sonde, to give the rocket a near vertical path. The second engine would need to kick in before the rocket slowed enough to point more than a few degrees off vertical. As long as the rocket speed is kept up above several times the wind speed, it will not weathercock much at all during the second engine burn... Since weather cocking is a function of the speed of the rocket vs the speed of the wind. So the second engine could be a low thrust, long burning engine without substantially increasing weathercocking. Mike is right that weathercocking can only happen during engine burn, but the effect is incremental at high rocket speeds.
This also sheds new light on the question of breaking the sound barrier. We know that exceeding the speed of sound increases drag tremendously, decreasing efficiency. So the more of the flight exceeds the speed of sound, the bigger and heavier the engine will need to be. The rocket might need added weight too, to help it coast against all that drag.
Ideally, the rocket will weathercock least, and be most efficient: If you accellerate at the maximum structural G limit of the sonde until you approach the sound barrier... which should happen in a little over 1 second. Then hold that speed with a very low thrust, slow engine burn. It might be possible to accomplish this with a K engine that has a special thrust curve... with a high innitial thrust, and then quickly settles into a slow burn... Or two smaller tandem engines. The advantage of using tandem engines is the the smaller 38mm diameter, which makes the rocket have less drag and weight, and fit in a smaller, lighter launch tube. Mike mentioned in his last Email, that he is experimenting with a new oxidizer that might make it possible to make 38mm engines longer, with more total impulse.
Cheers,
In the process of thinking through the tandem engine concept, I have spent a lot of time understanding the dynamics of weathercocking. At first, I accepted Mike's explanation about the rocket only weathercocking during the engine burn... which is true... But there is a bit more to it. I'm glad it is windy at my launch pad, because it forces me to deal with it. The other statement that is only sort of marginally true is that the safety factor space between the CP and CG effects weathercocking.
First Mike's statement. If you picture the rocket fired vertically from a cannon in a strong wind with no engine burn... The momentum of the rocket is vertical... so it will try to continue on that path. But the rocket with its fins, like the tail feathers of an arrow will always weathervane (point at the relative wind)... which is not the same as weathercocking (going up wind). The rocket will always point directly into the relative wind. When the rocket is going extremely fast, the relative wind is very vertical, so the rocket will point virtually straight with its track. As the rocket slows, even though it might still be moving directly vertically, it will gradually point farther and farther horizontal into the wind. When the rocket reaches apogee, it will be horizontal, pointed directly into the wind... even though its path has not strayed from a vertical line. (The wind should theoretically, gradually accellerate the rocket down wind, until it has a horizontal component equal to the wind speed. So even though the rocket weathervanes into the wind, its path is curved slightly down wind.)
Now picture the rocket under power in the first couple seconds of flight. Since the direction the rocket will point, is the hypotenuse of the vertical speed of the rocket, and the horizontal wind speed... the rocket will tend to weathervane the farthest off vertical when it is going the slowest... which is just after it leaves the launch tube. During this first fraction of a second of flight, the rocket is pointed off vertical... so the thrust of the engine is off vertical, and that begins to accellerate the rocket horizontally into the wind... weathercocking. As the speed quickly rises, the rocket quickly points more directly along its new path... so the thrust is now in line with the path. So the rocket will follow the new path in a relatively straight line... which is just what you see at the rocket meets.
This fits well with what Mike was saying about our needing to use a very high thrust engine. We want to minimize the time that the rocket is going relatively slowly in the first fraction of a second of flight. The longer the launch tube, the more vertical it will go in a strong wind as well.
Now to the other statement about the CG to CP spacing. The above weathervaning will occur no matter what the CG to CP spacing is. So the only effect it has is: A rocket that is barely stable might weathervane a tiny bit slower. Since the rocket has some yaw inertia, its weathervaning will lag slightly, as it begins to weathervane from its vertical allignment in the launch tube. This lagging will occur most, just as the rocket is leaving the launch tube. So this lagging does decrease weathercocking . Making the rocket longer would help, because it would have more yaw inertia. The effect of changing the CG to CP spacing is only slight, however. There are other effects regarding the CG to CP spacing that have a much greater effect... like safety, weight, and drag. A rocket that is marginally stable might be more likely to oscillate/wobble in the first second of flight. When the rocket does overcome its stationary yaw inertia, the rocket will yaw into the wind... but now the rocket's moving yaw momentum will tend to continue past its proper weathervane headding.
Applying all this to the tandem engine concept. It is crucial that the rocket accellerate real hard in the first second of flight. The first engine would need enough thrust to accellerate the rocket right at the structural G limit of the sonde, to give the rocket a near vertical path. The second engine would need to kick in before the rocket slowed enough to point more than a few degrees off vertical. As long as the rocket speed is kept up above several times the wind speed, it will not weathercock much at all during the second engine burn... Since weather cocking is a function of the speed of the rocket vs the speed of the wind. So the second engine could be a low thrust, long burning engine without substantially increasing weathercocking. Mike is right that weathercocking can only happen during engine burn, but the effect is incremental at high rocket speeds.
This also sheds new light on the question of breaking the sound barrier. We know that exceeding the speed of sound increases drag tremendously, decreasing efficiency. So the more of the flight exceeds the speed of sound, the bigger and heavier the engine will need to be. The rocket might need added weight too, to help it coast against all that drag.
Ideally, the rocket will weathercock least, and be most efficient: If you accellerate at the maximum structural G limit of the sonde until you approach the sound barrier... which should happen in a little over 1 second. Then hold that speed with a very low thrust, slow engine burn. It might be possible to accomplish this with a K engine that has a special thrust curve... with a high innitial thrust, and then quickly settles into a slow burn... Or two smaller tandem engines. The advantage of using tandem engines is the the smaller 38mm diameter, which makes the rocket have less drag and weight, and fit in a smaller, lighter launch tube. Mike mentioned in his last Email, that he is experimenting with a new oxidizer that might make it possible to make 38mm engines longer, with more total impulse.
Cheers,
