Mach 1 in its own length … no way!

Brian Blestowe set out to debunk the urban myth that a Mk2 Bloodhound missile reached Mach 1 (speed of sound) by the time it had cleared the launcher; he was successful!

The Mk 2 missile was only stressed to 35g in the longitudinal axis so Zero to Mach one in its own length (around 1700g) was a bit of Newton BS. Actual acceleration at launch was 19 to 21g dependent on the ambient temperature of the boost rocket motor propellant charge. Actual specs for the Gosling XV motor were 23,000 lbs for 3.8 seconds at -25°C to 31,500 lbs for 2.8 seconds at +40°C. The only firing that I do have information about in the UK was the Singapore round fired in 1980. It was fired at a sea level temperature of 12.6°C and an atmosphere pressure of 1007.3 millibars.

Boost motor separation was at 3.803 seconds after first movement at which point the missile was 1332.6 m (4536.1 ft) from the launcher in ground distance and 795.0 m (2608.3 ft) above the launcher at a speed of 701.0 m/sec (2299.9 fps) (1568.09 MPH, 1362.63 Knots, Mach 2.04373). At that point the missile angle to the ground was 29.060° and it had rolled to starboard 15° off the line of fire (which was 328°), which wasn’t a
surprise seeing that the Wind velocity was 5.182 m/s (11.59 MPH) from a bearing of 250° (almost side on to the line of fire). For hotter (and colder) temperatures, the Swedes fired one at -25° C from Vidsel, while all of the hotter ones would have been from Woomera.

The problems getting figures from those firings is most of them were done with the original Gosling IV motor planned for BH2, which only produced 22,000 lbs at -25°C and because of that was not capable of accelerating the missile to a speed where the ramjets could produce enough thrust to accelerate the missile post boost separation on a really cold day (which was bad news for sales to Sweden and Switzerland!).

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Brian is a BMPG member and the volunteer at Aerospace Bristol who has redied the Bloodhound Mk2 missile for exhibition. This is the only fully operational example that is complete; the only missile in UK to have fuze aerials and in every respect is the National Standard.

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More about Bloodhound Homing

Pete Murray gave an expansion as to how the homing methed was achieved.

A very rough outline (from memory):
  • A gyro mounted on the dish allows its stabilisation via the dish servo (decoupling it from missile motion).
  • A spinning antenna offset from the spin axis creates a conical scan pattern. The phase and amplitude of the received signal reveal the dish pointing error (direction and magnitude of target misalignment from boresight). The dish servo steers the dish, via precession of the gyro, to null the dish pointing error.
  • The output of the dish servo represents the sight line rate in pitch and yaw. Zero sight line rate implies that the missile will intercept the target. Thus, to achieve an interception, the missile flight path must be controlled to null the sight line rates.
  • The pitch and yaw sight line rates are resolved into pitch and roll errors for the wing control servo.
    The roll channel moves the wings differentially to control to the missile roll rate and null the roll error, which brings all the error into the pitch plane. The Pitch channel moves the wings together to control missile flight path, such that an acceleration (around a curved path) proportional to the error is achieved. How hard the missile manoeuvres for a given error is controlled by a navigational constant
Other Notes (again, from memory):
  • The missile was monostable in the pitch plane (it would only pitch only one direction).
  • The missile had a weathercocking motion in flight; hence, two accelerometers displaced as far apart as possible were used in the pitch feedback loop.
  • A gyro provided roll rate feedback.
  • The navigational constant was halved for engagements against receding targets.
  • Gravity created a one G bias on the accelerometer output, which had to be compensated for to prevent the missile coming to earth during low altitude engagements.
  • The missile had characteristic body twisting and bending moments, which had to be filtered from the roll and pitch control channels.
  • Sightline rates were heavily filtered until switched out via the command link.
  • Navigation was in bearing only until climb cruise was switched out via the command link.

The Bloodhound Homing Algorithm

Back in May Peter Wolstenholme kindly reminded the BMPG Group about the Bloodhound homing algorithm.

The method of navigating to the correct interception point is called “proportional navigation” and relies on measurement of sight line spin (sls). That is, if the missile’s dish is pointing in a fixed direction in space, and continues to do that, then the missile will intercept the target. Any need to precess the dish gyros is caused by an error in the navigation path, so the missile needs to change direction so as to servo the sls to zero. The course change is set to a few times the sls.  An interesting control problem, as the computed Miss distance is equal to the sight line spin divided by V t^2.  V is the missile velocity and t^2 is the square of the time to go. So the gain of the servo increases rapidly as one approaches the target. Of course, at interception, if not a direct hit, the s.l.s. becomes larger than the dish servo can track, but by then one is within fuze range.

Peter added, “I spent many hours running end-course simulations for Bloodhound 1 to fix the optimal parameters, around 1957. End-course meant the last 5 seconds. I was very impressed by the agility I observed of twist-and-steer, conferred by the low rotational moment of inertia as compared with  missiles which needed to pitch from rear-mounted control fins”.