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.

Our Aerospace Adviser Asks Questions.

Answering our Adviser’s Initial Questions.

Area_rule_unifilar_drawing.svg

Below is an exchange between our new adviser to the project (to be announced officially soon and myself (Robert Brand). Here are his initial comments and please remember that he has not seen anything yet. Our adviser is a pilot with an aerospace engineering degree.

Our Adviser  Hi Robert, Here are a few questions and thoughts.

1. Propulsion

At a first glance you may think you don’t have a propulsion problem, because the thing is falling down.

The fact is, you do. The basic forces and their components (lift, weight, thrust and drag) are always in balance as long as the aircraft is not accelerating in any axis.

This is valid the other way around as well: The aircraft will accelerate as long as the forces are not in balance.

For your case, you need to have the capability to accelerate beyond the sound barrier.

The problem is that the parasitic drag increases exponentially as you approach M=1 and because you are going at a certain angle towards the ground, a certain component of this force, or all of it if you dive vertically, adds to your lift. Once your lift becomes greater than your weight, you will start to slow down.

If this happens before M=1, you will never reach supersonic speed. If it happens after M=! you can further accelerate, because the drag drops after transonic. Transonic is the worst place to be. I order to be supersonic, you must achieve M=1 ASAP, before the air becomes dense.

If you drop from 33km, forget it, because at 30km you can already feel the effects of atmosphere.

The first thing you need to do is apply total surface design, or coke-bottling. The total surface of your craft must be consistent, so at the place where you have wings, your fuselage must be narrower. This dictates your fuselage to be in a shape of a coke bottle. This will reduce drag significantly.

Also, center of lift on the wings changes in supersonic flight and you need to cope with that. There are two strategies, variable wings or variable centre of gravity. I have a very original idea how to solve that.

2. Stability

Any object going through a fluid tends to assume a low drag position. Sometimes this low drag position means rotating and spinning.

You can solve this problem by active control (unless you have f-16 engineers on board, forget it) or aircraft design.

I would suggest delta wings, high swept. Delta wing has an inherent auto stability feature and high sweep angle to reduce drag and effect of the wings.

Accept it, your aircraft can be designed either for high speeds or low speeds, unless you have flaps or variable wing geometry.

———————

My Response

I look forward to how he views this and I will report back soon. I expect that I will have allayed most of his fears:

Firstly we are already applying the constant area rule. Even the A380 has aspects of the rule in the design. I lectured at Sydney Uni on the subject only a few weeks back. I understand the rule and some other rules to do with supersonic flight, although their effects are much less than the constant area rule.

Yes, the wings may very well be more swept back than in the image on the site. We will do drop tests to a certain the best wing shape and we have access to a wind tunnel.

The wings will be symmetrical (top and bottom)– ie zero lift. They will be therefore not an issue at supersonic speeds. The elevator will provide the “lift” with speed at lower altitudes. Yes, it will land “hot” – we may use “flaperons” ie combined flaps and ailerons. It should be noted that these are less effective as ailerons when they are biased down as flaps, but they will be bigger than needed. They will be symmetrical also. Flaperons are really ailerons  that are mixed with the flaps signal on the transmitter to bias them both “on” as flaps/ The ailerons do not work with the same efficiency when they are both biased down, but they do work. We may use separate flaps, we may not use flaps. Testing will determine the stability and best options.

Below is a video that shows how they mix the signals in the transmitter of radio controlled models to adjust the various control surfaces. This is a third party video

The spin will be counteracted by the large ailerons even in low air, the trick is to stop the spin in the first place by making the craft very symmetrical and test that aspect.

Our novel answer to controlling the need for different centres of gravity: We will have serious control of the centre of gravity in the craft and we will be able to move the batteries and electronics with a screw mechanism back and forward in the fuselage. This will keep the craft from being unstable at supersonic speeds. Once it goes back to subsonic, we will begin moving the centre of gravity back as we begin to level out the flight and slow the craft.

At slower speeds, we have air brakes that will slow the craft if needed

The supersonic spike at the front of the aircraft is used to create the shock wave with a pin point device ahead of the fuselage and ensure that the biggest part of the shock misses the wing entirely. A shock wave over the wing creates massive drag and this is why many pilots in the early days, tried to break the sound barrier and failed. The spike doubles as a VHF / UHF antenna

Three weeks ago we launched a payload mainly of wood, covered in bubble wrap for the electronics and, with the parachute deployed, it reached 400kph. For the event we will be using a Zero Pressure Balloon to get to over 40Km altitude. If the 9Kg of the payload are not enough, we will increase the weight and size of the craft. We will break the sound barrier, but need to show it is a fully working aircraft after the dive.

In World War II bombs from high altitude aircraft regularly broke the sound barrier. We will shift the centre of gravity well forward and act like a bomb. We should be able to punch through that barrier with a lot to spare – even Felix Baumgartner broke he sound barrier for his jump altitude of 39Km. He was not very aerodynamic. We expect to terminate supersonic flight at around 31Km

Yes, transonic is a bad place. We do not intend to allow the craft to stay there! Punch through while the air is super thin and keep accelerating!

Will we make Mach 1.5? – it depends on our launch altitude. We will achieve Mach 1 – the sea level speed of sound is our target. About 1200kph.

Area_rule_unifilar_drawing.svgThere is much more, but I expect that I have answered most of your questions in this email. We will be using ITAR controlled GPS units for supersonic tracking and also we will be using radar transponders to warn other aircraft. The Jason and I will be testing a lot of aspects of the flight with drop tests from balloons. I will be launching another balloon in a week’s time.

The picture above shows the constant area rule – efficiency is gained by the cross-sectional area of the aircraft being constant along its length. The fuselage gets thinner where the wings are as there area has to be accounted for. This rule is important as aircraft get close to the sound barrier and this is why Boeing 747 aircraft were so efficient.

Note the light blue area has to be the same as the dark blue area, including the area of the wings. This is the “coke bottle” shape that our adviser mentioned – note the thinner mid section of the central body.

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!: