Convair Defensive Anti-Missile System (DAMS)

[KJ_Lesnick]

...Also known as the Lenticular Defense Missile or Pye-Wacket.

The missile was designed to be launched omnidirectionally (forwards, backwards, sideways -- all directions) from the B-70, so as to protect the aircraft from enemy missiles and interceptors: It was designed to withstand acceleration loads of at least 60-250 g's, fly hypersonic and successfully intercept targets with relative velocities of up to Mach 7.  According to this website 250 g's could be achieved as low as Mach 3.

The guidance system was to initially come from the airplanes fire-control system (command-guided?), followed by an IR guidance system allowing itself to home to target.


My questions basically come down to the following

I: Basic Design

A: Which design is essentially correct?

1.) One design I've seen for the Pye Wacket was effectively a lenticular planform with a wedge cross-section as depicted here
2.) Another was a circular cross section with the exception of engines in the back and paddles for thrust vectoring

B: Would this design in anyway represent a production model?


II: Performance

A: Alpha & Sideslip: Do the angle of attack and sideslip figures seem genuine considering the stated speed, g-load, roll-rate, or do they seem to be either overly low?

B: Maneuvering Loads

1.) Since the listed maneuvering load is stated to be 250g at Mach 3, does that mean the missile's g-loads would stay the same as the mach number increases, or would the g-load simply keep building up?
2.) If the g-load kept building up, how much would it be at Mach 5?
3.) Can somebody tell me what mathematical formula could basically give me an idea of the equivalent g-load for different mach numbers (for example a missile pulling dozens of g's at Mach 6 could be out turned by a fighter at Mach 0.9 pulling 9) because I'd much rather just put the numbers together myself than pester all of you.
 

III: Guidance System

1.) Would this IR seeker have been more advanced than most IR seekers of the era?
2.) Could the guidance system actually keep up with the missile's maneuverability (say the missile could do 250g at Mach 3, could the guidance system deal with the degrees per-seconds encountered in that turn and hold the lock)?
3.) Could the maneuverability of this system have basically made it impossible for a fighter to successfully escape it?

[Hobbes]

II.B.1: There are two factors at work:
1. the maximum turn ratio. This is determined by the size of the control surfaces, etc. When you increase the speed, the max. turn ratio stays the same, so the G-load would increase. But this is limited by:
2. the structural strength of the missile.
if the specs say that 250g is the limit, it means that the structure won't withstand higher loads than this, so at higher speed they'll have to limit the turn ratio.

[KJ_Lesnick]

Hobbes

II.B.1: There are two factors at work:
1. the maximum turn ratio. This is determined by the size of the control surfaces, etc. When you increase the speed, the max. turn ratio stays the same, so the G-load would increase.

I don't know if this missile had control-surfaces per-se.  Some models had paddles for thrust vectoring which is both aerodynamic and thrust-vectoring in one; the other seem to emphasize RCS only...

But this is limited by: ... the structural strength of the missile. ... if the specs say that 250g is the limit, it means that the structure won't withstand higher loads than this, so at higher speed they'll have to limit the turn ratio.

Firstly, it said the test-vehicle's loads exceeded 250g for Mach 3 and higher velocites... (Section 2.13 in the link -- which I fixed).  That could indicate either a max-out at some g-load over 250 @ Mach 3 or an increasing build well after Mach 3 all the way up to max speed.

[Hobbes]

If there are no control surfaces, the turn rate is limited by whatever system is used to turn. Generally you can say that the missile can turn at X degrees per second. The G loading associated with that depends on the speed.

II.B.3: I'm no aerodynamicist, but my intuition tells me that this relationship would be linear. If it's 250 G at Mach 3, it'll be (5/3)* 250 G at Mach 5.

250 G sounds awfully high to me. The missile would have to be almost solid to withstand such forces. You're getting close to the loads experienced when firing an artillery shell.
IIRC the Aster missile can maneuver at ~60 G, and that's the highest G-load I've heard of.

[KJ_Lesnick]

Does anybody know the formula you'd use to determine the g-load produced by a turn rate at a given set of speeds.  When I say this I mean if I pull 60g at Mach 5, what g-load at Mach 0.90 would be needed to get the same rate of maneuver?

If I recall right the formula was like square root Mach number and so on...

[Hobbes]

a  = v^2/r
a = acceleration (g-load)
v = speed
r = radius of the turn

https://en.wikipedia.org/wiki/Centrifugal_force

[KJ_Lesnick]

Hobbes

I keep entering this and I can't seem to get any number that makes any sense... the number would be in decimals

[Mr.Creak]

It'll be SI units.
a  = v^2/r
Metres/ sec for v and metres for r.
Then divide the result by 9.81 to get g.

But, essentially, it shows that g increases with the square of the speed.

[KJ_Lesnick]

Mr.Creak

Tell me if I'm right here...

• a = v^2/r
  
• (2452.5 m/s) = (885.233 m/s)^2/r
  
• (2452.5 m/s) = (783637.464)/r
  
• (2452.5 m/s)(r) = (783637.464 m/s)(r)/r
  
• (2452.5 m/s)(r)/(2452.5 m/s) = (783637.464 m/s)(2452.5 m/s)
  
• r = 319.526 meters
  
• r = 1048.3104 feet
  

These numbers are based on the table for dynamic pressure in the linked article and I simply guesstimated where the dynamic pressure for Mach 3 would peak out and that seemed around 45,000 feet so the numbers are based around this.  I also did computations for a sea-level Mach 3 ride as well.  Regardless, the F-15 pulling 9g down at 475 KIAS would yield you a turn rate of 2190.543...

This thing would outmaneuver any fighter we have currently. The issue of course is the capability of the IR seaker.  Many of the seakers were only designed to track a certain number of degrees a second and for all I know the airframe's maneuverability could possibly exceed the seeker.  Considering necessity is the mother of all invention and it's surprising what kind of technological feats were doable even in the 1960's with state of the art technology, it might have been do-able.

What do you think?

[KJ_Lesnick]

The math works out, so I'm now wondering this...

This missile could turn well over 360 degrees a second.  The missile was to be command-guided from the launch aircraft (XB-70), after which it would go active using a heat-seeker.  Could the heat-seeker keep up with that kind of maneuvering?  I could be wrong here but most of them seemed to do around 15-20 dps.