 Bloodhound System
Bloodhound Going Like a Bat Out of Hell
Calculating the Distance for the Missile to Become Supersonic

Pete Murray
Various web pages claim that the Bloodhound missile was supersonic only a few metres from the launcher. However, the physics appears to say otherwise.

Calculating the time to become supersonic.
The speed of sound at sea level is approximately 340 metres per second.
The missile has a mass of approximately 5000lb and the 4 boost motors deliver approximately 100,000lb of thrust, so the initial acceleration is 20g, or 196m/s2.

If we simplify things a bit and assume that the acceleration remains constant, we can calculate that the missile becomes supersonic after 1.73 seconds.

Calculating the distance travelled.
Plugging the numbers into Mr Newton’s equation, d = ½ at2, gives a distance of 293 metres.

I’ve taken a few liberties here with assumptions and simplifications, but 296 metres is hopefully not too far off the mark. Does anyone know the actual numbers?

As a matter of interest.
The missile gyros were all subjected to a series of drop tests (20g I think) before final testing. Radio Frequency Units (RFU) were also drop tested and monitored to ensure that the local oscillators and IF stages remained stable during the deceleration.

The LCP Doppler prediction calculation coded into the LCP software assumes a missile velocity of 2400 feet per second at acquisition of the target (5 seconds after launch). This converts to 731 m/s or 1636 mph.