Randall Clague wrote: > OK - this matches both my observations and my intuition. But, I don't > see why this is so. Mathematically, it seems to me that a gravity > turn is independent of whether the vehicle is under power; and that , > second for second, the trajectory will look the same, powered or not. > What is different is the proportion of the flight that is powered. > > Can someone resolve this paradox?
Imagine an aerodynamically-stabilized unguided rocket that tends to align its airframe with the direction of its airspeed. Its thrust is always aligned with its airframe (i.e., the engine has no gimbals or other means of deflecting its thrust off axis). If we launch this rocket perfectly vertically and it stays vertical in flight, the thrust is always pushing upward. In this case there would be no directional difference between a long or short burn. Now, assume that at some point during the ascent, the rocket is deflected so that its airframe is no longer perfectly vertical. If this happens during powered flight, the thrust produced after that moment will not be in the same (i.e., vertical) direction as the initial thrust: it will tend to push the rocket sideways (relative to the vertical path) as well as upward, and its velocity will therefore come to have a horizontal component. The rocket, being aerodynamically stabilized, will tend to align itself with this new direction of motion, so its subsequent thrust will continue to accelerate it sideways as well as vertically. If the deflection happened in vertical coasting flight, there would be no "sideways" thrust, and the path would not be deflected. Next, consider a rocket launched at an angle (or one that begins to deviate from vertical in flight, as in the prior example). Gravity will be pulling it sideways (relative to its path) instead of merely opposing the thrust. Again, we have a change of the direction of its path, and thus a change in the direction of its thrust. (This will cause the flight path to continue to increase its angle from vertical.) >From this, we can deduce that the trajectory will depend on the thrust-time history as well as the initial launch angle - and (other factors being equal) the path of a long-burning rocket will be more influenced by differences in the initial launch angle (or by other perturbations, such as wind-deflection) than will that of a short-burning one. -dave w _______________________________________________ ERPS-list mailing list [EMAIL PROTECTED] http://lists.erps.org/mailman/listinfo/erps-list
