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# Flight vehicle pitching moment derivatives of velocity

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## Flight vehicle pitching moment derivatives of velocity

(OP)
I am interested in estimating the effect of flow acceleration on the pitching moment of a conventional aft tail monoplane. Often, discussions of this type concern themselves with Mach effects,  "Mach tuck" is often used to describe the transonic effects on the horizontal stabilizer generating a nose down Cm about the vehicles CG. However, this seems a quasi steady phenomina.
I am interested in a RATO launch where the vehicle is being linearly accelerated (RATO thrust aligned with the fuselage axis). There is a distinct nose down moment and it doesn't seem likely to be a Mach effect. The vehicle is accelerated from 0.0 to approximately 500 feet per second in 2.5 seconds. The duration of the moment variation lasts for approximately 90% of the flight to 500 fps. I.e. the moment increment asymptotes to zero as the vehicle's speed increases.
In your collective opinions, is it possible that there is an apparent mass effect operating here?
Does anyone have experience with the moments imposed on a fairly rapidly accelerating flight vehicle of conventional layout?
(the horizontal control surface has an 8%, and the wing a 12% thickness to chord ratio)

### RE: Flight vehicle pitching moment derivatives of velocity

is this a school problem ?

as for supersonic flight ... i believe the problem is the movement of the wing aerodynamic center requires a large change in h.stab trim, hence the "all flying tailplane".

i have a feeling that the h.stab is providing a balancing pitch moment (off-setting the low line of action of the RATO thrust) ?

### RE: Flight vehicle pitching moment derivatives of velocity

(OP)
I am not a student, just a working senior engineer who is new to RATO launched vehicles. I was fishing to see if anyone here has had RATO launch aerodynamic experience that might be applicable to my issue. I am sure that our thrust vector angles have been accounted for so, it would seem to me to be some type of aerodynamic interaction. Local flow entrainment has been vetted and CFD show little direct influence in the region of the horizontal stabilizers.
thus my focus on apparent mass effects since the vehicle accelerates pretty rapidly.

I am open to any new ideas. We thought it might be a ground plane interaction, but CFD has shown little influence from ground effect. The flight reaches 800 wing chord lengths in altitude within the 2.5 seconds.

Well, thanks for your reply. I do appreciate any assistance I can get. It will be enjoyable to figure this out.

### RE: Flight vehicle pitching moment derivatives of velocity

cool ... it was just the way you worded the question ...

i don't think "mach tuck" as any bearing on your problem ... though i could (easily) be wrong.  i think "mach tuck" is an issue with the overall airplane aerodynamics, that the centre of lift is moving a lot (and quickly) as the plane goes supersonic and this requires a large H.Stab input to balance out.

i was trying to think of how the forces on your RATO plane would work out ... at low speed the wings aren't producing enough lift, so something else is ... i suspect there is something in the pitch up of the plane, once the H.Stab is generating enough lift, Vmo, which allows the RATO thrust to react the airplane weight).

i don't understand the "apparent mass weights".

### RE: Flight vehicle pitching moment derivatives of velocity

Here's a nice pitcure of a RATO launch of a Ryan UAV

### RE: Flight vehicle pitching moment derivatives of velocity

500 fps is probably under mach .5 so mach effects are doubtful.

What speed is the trim of the A/C set for at launch, and is it adjusted during the acceleration?

I'd double check the thrust vector calcs just in case.

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