# Hypersonic Boost Glide Range

Looking at an article earlier about hypersonic boost glide vehicles and I noticed how small their L/D ratios were ~2.5/1. If they begin their hypersonic glide at 50km in altitude would they not travel forward 2.5km for every km they lose? Hence their range would be 50km * 2.5 = 125km, clearly this isn't correct and their published ranges are 6,000+km. What equations would one use to calculate their range since its not simply a matter of L/D.

• At high speeds the centripetal force cannot be neglected. Low earth orbit satellites move at 7.8 km/s and do not need lift at all to stay at the same altitude. Jul 12 at 9:41

Gliding implies that lift equals weight.

This is not the case for hypersonic boost glide vehicles. They ascend like rockets during the burn phase (or are carried aloft by a rocket) and then fly mostly, but not fully, ballistic after their engine has shut down (rsp. have been released from their carrier). In contrast to a conventional reentry vehicle, they are designed to create aerodynamic forces perpendicular to their flight path for trajectory modification. This allows them to boost their range a bit, hence the name, which is more efficient than creating the same force with a rocket. However, the major reason for their use of aerodynamic steering is to make their final trajectory harder to predict.

Hypersonic soaring was initially proposed by Eugen Sänger to stretch the range of a hypersonic rocket plane. By "dipping" into the denser atmosphere and creating enough lift for a trajectory change up into near-space, it was hoped to fly halfway around the Earth. The US research program that lead to the Boeing X-20 "Dyna Soar" was an application of this idea. However, the heat loads in the lift phase are too high for current materials. Only instationary hypersonic flight with either ablative coatings or heat sinks is so far possible.

When the engine stops, the craft is still travelling upwards at a steep angle. In the thin atmosphere at 50 km, its trajectory is more or less ballistic and takes a while to reach its zenith, turn back down and enter thicker air where its glide ratio takes over. During that time it has travelled a long way.

It can then trade its high speed for extra lift, by increasing its AoA and effectively trying to climb back out, slowing itself down in the process. The poor gliding angle is then relative to that "virtual" climb flightpath.

This is a very interesting question from the other end of the gliding spectrum.

We must consider the two friends of gliders, altitude (potential) and speed (kinetic) energy.

An incoming hypersonic vehicle is blessed with both. Much of its low lift to drag ratio is due to its very high velocity. So it would glide more effectively by trading speed, rather than altitude, as "fuel" against drag at first, then use its wing and altitude for maximum range. This was the approach the Space Shuttle used to re-enter and land from thousands of miles away.

For military purposes, obviously it wants to keep its speed for as long as possible to avoid interception.

The end design is applications driven.

• After some further suggested digging (this question was cross-posted on Reddit) I came across the following equation for general hypersonic boost glide gliding ranges, its in this paper on page 10: link Jul 14 at 15:30

From a congressional briefing on the subject:

Hypersonic glide vehicles (HGVs), like all weapons delivered by medium- and longer-range rocket boosters, can travel at speeds of at least Mach 5, or about 1 mile per second.The key difference between missiles armed with HGVs and missiles armed with ballistic reentry vehicles (i.e., those that travel on a ballistic trajectory throughout their flight) is not their speed, but their ability to maneuver and change course after they are released from their rocket boosters.

So yes, the hypersonic glider does have a worse L/D ratio than an aeroplane, still better than a ballistic missile though.

• One may wonder how well a 1 mile/second object can turn, especially in thin air. Jul 12 at 12:24