@llDeadboyll Basically, bombs in SimplePlanes experience an acceleration from drag equal to -0.05*velocity, so you can break a bomb's net acceleration into two components (horizontal and vertical) as ax = -0.05*vx (acceleration from drag) and ay = -9.81 - 0.05*vy (acceleration from gravity and drag). I solved these differential equations to yield functions for horizontal and vertical positions based on time and initial conditions (initial horizontal and vertical velocities and initial altitude relative to the target). Assuming a bomb is detached with no applied impulse (0% detachment force) these initial conditions are equal to the velocities and altitude of the aircraft at the time of release, which we can easily reference as standard Funky Trees flight variables.
I wanted to use the altitude vs. time relationship to find the time of impact, because then I can plug that time into the horizontal position vs. time relationship (which finds where the bomb will impact) and the target position predictor (which finds where the target will be at the time of impact). However, the altitude vs. time equation is not conducive to analytical root-finding (which would give me time to impact), so I can’t just plug in initial conditions and get the time to impact.
However, if we assume no drag, we can use simple kinematic equations to find an approximate time to impact, as these equations do allow for root-finding through the quadratic formula. But in most cases we cannot ignore drag, as doing so will yield an inaccurate result. So what I did was I set up a MATLAB script that calculates the time to impact using both the simple kinematic/parabolic model and the actual differential equation-derived model for a variety of combinations of initial vertical speeds and initial altitudes. Then, for each set of results, I divided the actual time by the parabolic-derived time to find the “corrective factor” that represents what you need to multiply the parabolic-derived time by in order to get the actual time to impact.
(1/2)
@llDeadboyll With all these different corrective factors for a wide variety of initial conditions, I then performed a surface-fitting operation to find a general function that takes initial vertical speed and initial altitude to compute an appropriate corrective factor. In SimplePlanes, all we need to do is then write out the quadratic formula that yields the approximate time to impact and then multiply this by the equation that computes the corrective factor to get a reasonably accurate result for time to impact. As I said earlier, this time to impact then goes to the target position predictor and the bomb impact point predictor, which describe where to draw the green and red indicators (respectively).
That’s basically the short explanation (yes, I know, not really short) but at some point I want to make an in-depth YouTube video that will go over all the fine details. I'm pretty busy irl though so I don’t know when I’ll get around to that.
(2/2)
@SomeSPGuyWhoLikesLore I can only hope that Andrew smiles favorable upon me...
+1@llDeadboyll Basically, bombs in SimplePlanes experience an acceleration from drag equal to
-0.05*velocity, so you can break a bomb's net acceleration into two components (horizontal and vertical) asax = -0.05*vx(acceleration from drag) anday = -9.81 - 0.05*vy(acceleration from gravity and drag). I solved these differential equations to yield functions for horizontal and vertical positions based on time and initial conditions (initial horizontal and vertical velocities and initial altitude relative to the target). Assuming a bomb is detached with no applied impulse (0% detachment force) these initial conditions are equal to the velocities and altitude of the aircraft at the time of release, which we can easily reference as standard Funky Trees flight variables.I wanted to use the altitude vs. time relationship to find the time of impact, because then I can plug that time into the horizontal position vs. time relationship (which finds where the bomb will impact) and the target position predictor (which finds where the target will be at the time of impact). However, the altitude vs. time equation is not conducive to analytical root-finding (which would give me time to impact), so I can’t just plug in initial conditions and get the time to impact.
However, if we assume no drag, we can use simple kinematic equations to find an approximate time to impact, as these equations do allow for root-finding through the quadratic formula. But in most cases we cannot ignore drag, as doing so will yield an inaccurate result. So what I did was I set up a MATLAB script that calculates the time to impact using both the simple kinematic/parabolic model and the actual differential equation-derived model for a variety of combinations of initial vertical speeds and initial altitudes. Then, for each set of results, I divided the actual time by the parabolic-derived time to find the “corrective factor” that represents what you need to multiply the parabolic-derived time by in order to get the actual time to impact.
+1(1/2)
@Johnnyynf thanks for the suggestion, that's exactly what I needed.
Also added 'funky trees' tag.
+1@llDeadboyll With all these different corrective factors for a wide variety of initial conditions, I then performed a surface-fitting operation to find a general function that takes initial vertical speed and initial altitude to compute an appropriate corrective factor. In SimplePlanes, all we need to do is then write out the quadratic formula that yields the approximate time to impact and then multiply this by the equation that computes the corrective factor to get a reasonably accurate result for time to impact. As I said earlier, this time to impact then goes to the target position predictor and the bomb impact point predictor, which describe where to draw the green and red indicators (respectively).
That’s basically the short explanation (yes, I know, not really short) but at some point I want to make an in-depth YouTube video that will go over all the fine details. I'm pretty busy irl though so I don’t know when I’ll get around to that.
(2/2)