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!

 Altitude vs temperature pressure densityDensity 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 and see it with a white background! 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.

Air Pressure, Altitude, Balloons and Rockets

Air Pressure and how it Affects Balloons and Rockets

Weather Balloon Burst

By Robert Brand

Rockets

One of the big issues for rockets flying to space is the air pressure it must climb through. As a rocket climbs it gets faster and has to push more air out of the way. As it goes higher the air thins and you can see from the table below that it is exponential. Have a look at the 1/100th  fraction of one atmosphere below and you will see that the atmosphere is 1% of sea level. The change is not linear. The atmosphere thins to a tiny percentage at twice that height, but at half the height it is 10% of the sea level pressure.

NASA says: The velocity of a rocket during launch is constantly increasing with altitude. Therefore, the dynamic pressure on a rocket during launch is initially zero because the velocity is zero. The dynamic pressure increases because of the increasing velocity to some maximum value, called the maximum dynamic pressure, or Max Q. Then the dynamic pressure decreases because of the decreasing density. The Max Q condition is a design constraint on full scale rockets.

fraction of 1 atmosphere (ATM) average altitude
(m) (ft)
1 0 0
1/2 5,486.3 18,000
1/3 8,375.8 27,480
1/10 16,131.9 52,926
1/100 30,900.9 101,381
1/1000 48,467.2 159,013
1/10000 69,463.6 227,899
1/100000 96,281.6 283,076

The Falcon9 reaches the speed of sound at 1 min 10 sec into its flight and then reaches Max Q just 8 to 13 seconds later depending on speed,and air pressure variables. Unlike airplanes, a rocket’s thrust actually increases with altitude; Falcon 9 generates 1.3 million pounds of thrust at sea level but gets up to 1.5 million pounds of thrust in the vacuum of space. The first stage engines are gradually throttled near the end of first-stage flight to limit launch vehicle acceleration as the rocket’s mass decreases with the burning of fuel.

Want to know more? This is not full of maths, just some fun stuff about Max Q and reaching orbit.

Balloons and Project ThunderStruck

Well for balloons we have a different issue. Balloons have to displace their weight in gas in the atmosphere and that includes displacing enough gas for the weight of the payload too.

Rate of Climb - Fall vs TimeThe climb to maximum altitude for the most part is linear. I discovered this when analysing the stats from my first balloon flight. It was linear until it reached the point that the balloon exploded. If you launch a balloon that does not explode, it will slow its climb and then float. My best guess is that as the climb becomes more difficult due to the air thinning thus and thus the displaced gas is getting closer to the weight of the balloon and payload, but the air resistance is getting less. The size of the balloon is also increasing with height and has to push away a greater volume of air to climb, but the number of air molecules in the increased mass is way less. All up it produces a fairly linear climb. The graph (left) from uplift-1 shows he linear climb and the exponential fall with the parachute deployed. For the parachute, the air gets thicker as it falls and thus slows more as the altitude decreases. Note the initial glitch was caused by a strong thermal just as we let go of the balloon. Once out of the thermal the climb was very linear. It is obvious when the balloon burst.

Altitude and Air PressureAnother view of th same data is shown on the left from UpLift-1′s flight. Note that the rate of climb is linear, but increasing slightly. This would be affected by balloon size and fill amount. The rate of climb may be fast, slow or medium, but that will also change the rate of change of the volume. Not all graphs are the same, but they tend to be similar. Note also that the size of the parachute needs to change with the weight of the payload. The ideal speed for the average payload would be about 5mto 6m per second at the landing altitude, thus landing at Denver, Colorado, USA will require that you make the parachute a little bigger since it is nearly 2Km above sea level and the air is noticeably thinner.

There are good fill charts on the web allowing you to calculate the size of balloon and the amount of Helium or Hydrogen to determine the altitude at which the balloon will explode. More on that another time. The picture at top of page is a weather balloon exploding at altitude.

All up, air pressure can destroy a rocket if its speed is too great and it will destroy a weather balloon if the air pressure gets too low. Both rely on understanding the effects of air pressure, but the dynamics are totally different.

Project ThunderStruck will use weather balloons for testing and they may explode. ThunderStruck‘s record attempt will be using a Zero Pressure Balloon to climb to or beyond 40Km.

Too finish off the post here is a video of a balloon burst. They are spectacular, especially as the balloons grow to a huge diameter and fill the screen of most wide angle GoPros!: