Talk:Reeves AN/MSQ-77 Bomb Directing Central

AN/MSQ-77 Modeling Errors

Bomb release velocity: The BTG simulation used A/C velocities prior to bomb release, so although the A/C flew somewhat steady, the actual release velocity differed due to perturbations (e.g., wind gust at release), velocity corrections not processed by the BTG, and for salvo releases (e.g., B-52 wing and fuselage bombs) the climb rate as the bomb load lightened. (The AN/MSQ-77 could control fighter-bombers conducting toss bombing.) Salvo releases also caused the mean bomb release position to differ from the track position used to command bomb release.
Bomb release delay: In addition to error in the release delay, errors in the modeling used in the bomb release algorithm reduced bomb release timing accuracy, e.g., modeling errors causing predicted impacts inaccurately closer to the target would delay release until after a more accurate release point.
Bomb release position: ECC at the simulated bomb impact was based on the simulation's last BRP (actual A/C position when integration ended), so shorter bomb runs placed the integration end nearer the actual BRP for lower ECC error (lateral bomb run directions relative to the radar beam also reduced ECC error).
Drift error: Crosswind acceleration on the bomb(s) was not constant despite being estimated from the constant drift angle provided by the aircrew. Drift error included the delay for the airsteam to effect ordnance released within bomb bays, as well as the delay for salvo-released bombs to separate and have individual aerodynamic loading not affected by the other bombs.
Integrator error: Different simulation rates for computing velocity and position were acceptable when the 6 integrator amplifiers were aligned within tolerances. For example, an out-of-tolerance 1% faster integration for the altitude position output over a 30 sec fall time (0.3 sec) at 600 mph (970 km/h) groundspeed would result in an earlier simulated impact about 264 ft (80 m) short. This horizontal simulation error caused by the vertical electrical error resulted in the separate AN/MSQ-77 bomb release algorithm comparing the target position & shorter simulated impact and delaying the actual bomb release point from nominal for a physical overshoot by about the same amount.
Targeting error: Target estimation error from the DASC was ~16 ft (4.9 m), and the AN/MSQ-77 site position also had error (e.g., slight coordinate system differences for the target and radar coordinates). For example, the LS-85 site estimation after the Heavy Green installation included surveying of nearby peaks' points followed by a "fly-in" conducted for LS-85 geolocation with LS-85--tracked aircraft overflying the points (surveyors on the peaks observed the flyover precision).

I tweaked the recent anonymous edits and moved the corresponding quote box and math equation section here for discussion. That content is generally accurate and sourced, but seems to me to be a bit too much detail. If it's not, it can be moved back -- particularly if similar pages have the corresponding level of detail. 30 SW (talk) 20:13, 14 July 2012 (UTC)

$\mathbf {r_{impact}} (t_{5})\approx \mathbf {r_{SBI}} (t):=\mathbf {r_{A/C}} (t)+\mathbf {\Delta } \mathbf {r} (t_{1},t_{2})$ for ${t>t_{2}},\quad$ where $\mathbf {\Delta } \mathbf {r} (t_{1},t_{2}):=\int _{t_{1}}^{t_{2}}\left(\int _{\tau _{1}}^{\tau _{2}}\mathbf {a} (\iota )d\iota \right)+\mathbf {v_{A/C}} (\tau )d\tau$

where

r = East (X) and North (Y) position from radar and height above earth (Z) for actual/simulated bomb impact and for radar-measured aircraft position (simulated BRP)

Δr = simulated displacement of the bomb caused by simulated accelerations and velocities during the trajectory

t = time during bomb run, e.g., start and end of the analog integration (t₁ & when Z_bomb=Z_target, t₂) as well as
     t₃ time to command the release, t₄ actual bomb release, and t₅ at actual impact

τ,ɩ = integrator simulation time (e.g., the 3 velocity-to-position integrators had slightly different simulation rates dτ_h, dτ_N, & dτ_E)

a = the modeled accelerations on the bomb that are integrated during the simulation to compute changes in simulated bomb velocity

v = time-varying A/C velocity used throughout the integration time, τ, to simulate the bomb release velocity

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