Breaking Mach 1, but by How Much?

A Zero Pressure Balloon fill_2610Hitting the Mach.

by Robert Brand

The aim of Project ThunderStruck is hitting Mach 1 and a bit more for good measure. Basically breaking the sound barrier. We may reach Mach 1.5, but that will be very much related to the height we reach with the balloon and few other factors. Project ThunderStruck is about Breaking Mach 1 – anything faster is a bonus.

ThunderStruck will rise to 40Km or more for its record attempt. It will need to use a Zero Pressure Balloon capable of reaching 40Km plus carrying a payload in the region of 20Kg including cameras and electronics on the Balloon.

Thanks to http://hypertextbook.com/facts/JianHuang.shtml for the information below regarding Joe Kittinger’s Record Jump in 1960:

Captain Kittinger’s 1960 report in National Geographic said that he was in free fall from 102,800 (31.333Km) to 96,000 feet (29.26Km) and then experienced no noticeable change in acceleration for an additional 6,000 feet (1.83Km) despite having deployed his stabilization chute.

The article then goes on the mention that he achieved 9/10ths the speed of sound and continued to suggest (with maths) that he would have broken the speed of sound with an additional 1,300 m (4,200 feet) of free fall.

If we assume an average acceleration of 9.70 m/s2, it is a simple matter to determine the altitude at which a skydiver starting at 40 km would break the sound barrier.

 maths to calculate altitude at which the sound barrier is broken

That’s an altitude of about 116,000 feet or 35.36Km. So how fast might we go starting at 40km altitude?

maths to calculate the max speed from altitude

Sorry if the equations are difficult to see – that is the quality from the website.

This is nearly 200 m/s faster than the local speed of sound. At the incredible speeds we’re dealing with, air resistance can not be ignored. A maximum of Mach 1.3 seems very reasonable for a human in a pressure suit compared to the prediction of Mach 1.6.

Given that the altitude of the glider release will be 40Km or more, then a top speed of near Mach 1.5 is possible. If we go higher, then we go faster.

Why is ThunderStruck an Aircraft?

Why is it considered an aircraft if it is in free fall with little to no drag? Simply because it is designed to use the little airflow to stabilise itself. Like and aircraft at lower heights uses its control surfaces for stable flight, ThunderStruck does the same. As you might remember from the jumps in the past by Joe Kittinger and Felix Baumgartner, they had serious trouble controlling spin. ThunderStruck will use the exceedingly thin air to control the spin and other forces acting on the craft during its record breaking dive.

After the dive and breaking the sound barrier, ThunderStruck will pull out of the dive under the control of RC pilot Jason Brand (12 years old) and level off, washing off excess speed. It will then fly to the ground under manual control to land just like any other aircraft.

This piece on Felix Baumgartner from Wikipedia:

203px-Felix_Baumgartner_2013Felix Baumgartner; born 20 April 1969, is an Austrian skydiver, daredevil and BASE jumper. He set the world record for skydiving an estimated 39 kilometres (24 mi), reaching an estimated speed of 1,357.64 km/h (843.6 mph), or Mach 1.25, on 14 October 2012, and became the first person to break the sound barrier without vehicular power on his descent.

Baumgartner’s most recent project was Red Bull Stratos, in which he jumped to Earth from a helium balloon in the stratosphere on 14 October 2012. As part of this project, he set the altitude record for a manned balloon flight,[8] parachute jump from the highest altitude, and greatest free fall velocity

The launch was originally scheduled for 9 October 2012, but was aborted due to adverse weather conditions. Launch was rescheduled and the mission instead took place on 14 October 2012 when Baumgartner landed in eastern New Mexico after jumping from a world record 38,969.3 metres (127,852 feet and falling a record distance of 36,402.6 metres. On the basis of updated data, Baumgartner also set the record for the highest manned balloon flight (at the same height) and fastest speed of free fall at 1,357.64 km/h (843.6 mph), making him the first human to break the sound barrier outside a vehicle.

This piece on the Speed of Sound from Wikipedia:

The speed of sound is the distance traveled per unit of time by a sound wave propagating through an elastic medium. In dry air at 20 °C (68 °F), the speed of sound is 342 metres per second (1,122 ft/s). This is 1,233 kilometres per hour (666 kn; 766 mph), or about a kilometer in three seconds or a mile in five seconds.

The Speed of Sound changes with altitude, but surprisingly this is not due to density or pressure, but with temperature!

512px-Comparison_US_standard_atmosphere_1962.svgDensity and pressure decrease smoothly with altitude, but temperature (red) does not. The speed of sound (blue) depends only on the complicated temperature variation at altitude and can be calculated from it, since isolated density and pressure effects on sound speed cancel each other. Speed of sound increases with height in two regions of the stratosphere and thermosphere, due to heating effects in these regions.

You can click of the image  (left) to enlarge the image. For the purposes of this flight, we will be using the speed of sound at sea level.

Will there be a Sonic Boom?

Yes, but it will not likely to be heard. In fact there will be two. One as it breaks the sound barrier and goes supersonic and one again as it slows to subsonic. Givent he size of the craft and the distance and thin atmosphere, it is unlikely to be heard from the ground.

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