Kinematic lead in LCOS
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Hi guys
Less of an actual mod question and more of a math/theory question that I am trying to understand for myself.
According to the manual containing this diagram, kinematic lead is defined as “The continuous change in position between the target and the F-15; a function of pitch, yaw, roll and acceleration of the F-15 combined with bullet TOF.”
Since the mode in question is the LCOS mode, meaning no radar track to provide target velocity vector, I’m guessing it uses the F-15’s pitch/yaw/roll and target range to calculate the target velocity. But I’m not understanding how acceleration (G force I assume) fits in. I tried fitting just pitch/yaw rate in radians/sec * target distance to get target velocity, which I then multiplied by bullet TOF and used atan2 with target range to get deflection angles, but they were far smaller in my actual HUD display compared to what I saw in an actual video of an LCOS display. Anyone here who could shed a little light on the subject? -
Not sure how much background you have for this but the math is encouraging.
When flying straight and level, the view from the HUD is an inertial reference frame. When you start turning (experiencing G, acceleration) the view is now a non-inertial reference frame, and centrifugal forces exist. The cannon shells are going to experience the same effective acceleration the pilot feels, so your ballistics will change.
Your math is assuming the shells don’t have a ballistic trajectory. In your non inertial frame, the aircraft are both staying where they are, and the shells are accelerating “down” from the pilots perspective. So you need additional lead, which is a function of the acceleration (and the time of flight).
From the inertial reference frame, The aircraft are accelerating constantly, while the shells are accelerating at 1g down (gravity).
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You are talking about gravity drop and trajectory shift, not kinematic lead. I already have those two accounted for. The kinematic lead is purely associated with the target motion, not my ownship’s effect on the bullet trajectory along with gravity.
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What manual is that from? Looks like rather an interesting read.
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As youve doubtless ascertained, Im not a ballistics expert. Pardon a little thinking aloud.
LCOS assumes a stable solution, no? Tracking, not snapshots. So the target is stable, and the shooter is stable. All factors other than kinematic lead, taken collectively, tell us where the bullet will be after one TOF. Those factors plus kinematic lead give us the solution desired?
The kinematic lead is then just the difference between the target position at the trigger pull, and the target position after one TOF. LCOS specifically assumes the target is being tracked with the pipper, that target acceleration remains constant, and shooter airspeed, G, range and POM remain constant during the bullet TOF. So kinematic lead is the lead required to account for the target motion. So… the only information available is range (and ownship parameters). With those assumptions, there is apparently enough information to calculate the target movement.
I guess the simplest scenario to imagine would be the target fixed in relative position from ownship (from the HUD view). The enemy aircraft turns at 18 degrees/sec, we also turn at the same rate, keeping them fixed at the same spot on the windscreen. Range remains constant, airspeed remains constant. In that scenario, theres a clear relationship between our parameters and theirs, and therefore we can determine their future position after one TOF pretty easily (velocity and acceleration). I dont use LCOS typically, but Im sure if I did that it would make this much easier to think about. The question Im stuck on is, is there a clear relationship between the target parameters and ours for any other condition? Is the key assumption, that the target is under the pipper, and the parameters remain constant, true for conditions where the target is not fixed in relative position from ownship? If not, that seems like it makes the kinematic lead relatively simple.
It seems likely to me that there is only that one scenario to consider. For range must remain constant, which in turn means airspeed must be constant, zero closure rate…
For the above scenario, both aircraft will be turning about the same turning circle. For a set of range, airspeed and G, there is only possible position for the enemy that occupies the same turning circle as us. Assuming they remain in the same TC as us, with the same airspeed, and turn rate, they will advance around the circle in a predictable fashion. If we know our airspeed and G, we know our turn radius. Knowing turn rate, we know how far along the circle the enemy will be at any future point. If we knew the TOF to start with, we could figure out where they will be at the TOF and that would be the kinematic lead. Im not sure we know the TOF until we know the kinematic lead?
I dont know if my musings helped you at all, but the relationship with the circle seems like a key one for this problem, to me (the untrained outsider).
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That definitely says “target acceleration”. An accelerating target won’t be in the same position one TOF later (and TOF may be variable) as one with constant velocity. Positive tangential acceleration is obvious in that you must increase the lead. Negative tangential acceleration would decrease the lead. A target accelerating radially toward has more interesting effects, TOF is decreasing, angular rate per linear speed increases, velocity vector changes.
As far as the calculated number being less than the displayed one. The term “trajectory shift” is unaccounted for. The airplane isn’t moving purely along the gun bore. The rounds aren’t emitting from the gun along the gun bore line. It’s throwing a baseball from a moving car all over again. The rounds have an initial velocity not from the real bore but the “effective bore.” If you are standing on the ground and want to throw a ball to someone in a moving car the lead computation is as expected. But take the same receiver and if you are in a car moving the opposite way your lead must be greater.
Try searching this book for “trajectory shift” and “effective bore” https://books.google.com/books?id=81krAQAAMAAJ
In fact this book https://books.google.com/books?id=q6xEAAAAIAAJ sums it up nicely on page 16. There is target deflection and there is gunner deflection. There’s an aiming component due to target motion and a component due to gun motion. -
Sorry. Wrong thread.
Sent from my SAMSUNG-SM-T818A using Tapatalk -
On the up side Frederf, I don’t think it’s all that complicated, as the target acceleration is assumed to be the same as ours, in LCOS, I believe.
Its the same set of information as level three EEGS, but a bit less sophisticated.
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Different types of LCOSS may use assumptions derived without radar data or with. In principle any is valid and most of the same details apply. I speak in general so I don’t know about F-15 or F-16 in particular.
I thought about it and I wanted to connect “pulling G” with seeing the bullet stream dip downward equivalent to a gravitational field proportional to the turning load factor but it didn’t sit right. Naruto’s intuition is good that flinging bullets at the point in the sky shouldn’t matter how the shooter is rating his nose or not. The devilsome detail wasn’t the angular rate of the gunner but his motion orthogonal to the bore.
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Well, pulling g is going to cause the bullet stream to dip downward, due to the centrifugal force. So that is going to be a factor in your solution. It’s just not a part of kinematic lead. Pulling g increases your AoA, which in turn causes the gun to be offset from the velocity vector, which means there is trajectory shift.