Trimming ThunderStruck for Speed

X2 shadow Trimming ThunderStruck Needs Extreme Knowledge

by Robert Brand

This post is very technical. I will try and make it a little easier to understand. I will not go into very deep into the various aspects that slow the craft, nor will I get into every aspect, just the major aspects that will cause us issues.

Designing a supersonic aircraft needs knowledge of supersonic aspects of airflow and pressure/shock waves. In a previous post we looked at the basic limiting factors and those important to getting us past Mach 1. This post will look at other factors that will cause us to make small changes to ThunderStruck to ensure we reach the maximum speed possible and get as close to Mach 1.5 as possible. We previously discussed the following:

  • Varying gravity due to altitude
  • The angle of the nose cone
  • The width of the fuselage
  • Altitude
  • Vehicle mass
  • Wing and Vehicle Drag Coefficient
  • Reference Area of the object in the direction of motion

In this post we will now look at other aspects of the design that will slow the crafts acceleration during its flight:

  • Base Drag
  • Area Rule
  • Transonic Wave Drag
  • Supersonic Wave Drag
  • Friction Drag

These factors take into account compressible air flows and incompressible air flows. Look them up, but simply Transonic and supersonic flows are compressible, subsonic flows are incompressible.  They are reflected in the items above.

If you would like to look at the Maths for these issues, there is a great document from Sydney University that can be viewed on the link below:

http://web.aeromech.usyd.edu.au/AERO2705/Resources/Research/Drag_Coefficient_Prediction.pdf

Base Drag

My knowledge here comes from rockets – same as the document. A flat based rocket does not have Base drag when it is firing its engines as the air flow does not have a pressure problem when compared to having a flat rear end! Below is a snapshot of the pressure differentials at the rear of the craft. There are more and bigger pressures not shown here, but you can clearly see the problem. as a rocket flies horizontally with its engines ignited, there is no void. The moment the engine ceases ignition, these pressure waves appear – Base Drag.

X2 Base Drag Pressure snapshot

Looks like a tapered fuselage at the rear of the craft is super important to acceleration towards the ground and again as the craft decelerates due to the thickening air density. It will need to taper from half way along the main wing part to the rear and go from 300mm to 50mm– enough for a parachute to be deployed – about 50mm. Whether we add a tapered cap, taking the final taper to a point for even less drag is not important at this stage. It will look better without the cap in drawings.

This important diagram from the linked document. This shows the flight of a rocket accelerating to Mach 1.6 (Dashed blue line) and then decelerating to to low speed (the solid black line). All the various drag issues are in this typical diagram. Base drag however is the difference between the two. There is no base drag during the rocket burn and then there is base drag once the engine ceases ignition.Drag issues in Transonic and Supersonic Flight

By gently tapering the fuselage to a point, we avoid disruption the boundary layer and any turbulence. For the X2 ThunderStruck flight the fall and acceleration will also look like the deceleration. Base drag will almost be eliminated.

Area Rule

We have spoken about this in an earlier post. That is keeping the cross-sectional area of the craft constant – so thinner where there is space (area) allocated to the wings. Area ruling will be somewhat addressed by the taper to the rear as discussed above in Base Drag. It is a fairly small effect unless you were spending significant time near the speed of sound. The X-2 ThunderStruck craft will spend 15 seconds between Mach 0.9 and Mach 1.2. I believe that it will be small and this is where the area rule has the biggest effect – but still small. There will be no additional change for area rule.

Transonic and Supersonic Wave Drag

The taper of the rear of the craft will minimise Wave Drag – both Transonic and Supersonic. Some playing with Wing Design may change the Wave Drag, but we will ignore it at this stage. I am not looking to play with the design unless there is a strong case. In the diagram above the Transonic Wave Drag begins at about Mach 0.9 and Mach 1.2 and Supersonic Wave Drag continues upward from that point.

Friction Drag

Friction drag occurs at low speeds with laminar flow being disrupted and the airflow becomes turbulent. We will have stalled at that stage and thus this is of no interest since we have an aircraft. We should have landed! This is ignored.

Trimming the Design

We have determined that we need to do two things. Stop the leading part of the winglets from protruding in front of where it joins the wing and to taper the fuselage. We will provide a picture of the new design shortly. Here is a render of the current X2 design without the new modifications:

X2 - Clouds2

The X2 ThunderStruck craft will have minimal impact regarding its maximum speed. I will reveal the new graphs shortly showing the speed at any given altitude point. As the air is extremely thin at our launch altitude, the increase in drag above 35km from the items above will not likely to be affect our top speed much as previously calculated, but may increase the deceleration slightly. That is the max G force as we slow. I will publish the updated results soon.

Finally a scan of the pressure waves from front to back on the X2 craft before we trim the craft:

X2 Pressure_Cut_Raised

Calculating Maximum Speed in Free Fall

100km accelerationFree Fall Speeds

by Robert Brand and Todd Hampson

Oddly enough, there is very little information on the web for calculating the maximum speed that a craft will fall from a specific height. It is a complex calculation requiring knowledge of the shape of a craft, the size of the craft, the amount of gravitational attraction at each height, the thickness of the atmosphere and the mass of the vehicle.

Todd Hampson has done some great work in getting the information together although he has not found a simple formula for calculating atmospheric density. He has temprarily used look-up tables and that has caused some rather “jerky” graphs. He will work on embedding a formula into the equations and removing the problematic look-up tables. None the less, this is a story of our travels and thus our problems too. Eventually it will be our triumphs too, but a bumpy chart is not a major worry to me, especially as we already know the solution. Now for the fun stuff.

Calculations, Calculations and More Calculations

Getting something “just right” the first time is near impossible and this is no different. Lots of complex data and no simple formula for air density, simply because it is not linear and non anything else. Tomorrow we will add the formula into the data and smooth out the bumps.

Today let us look at the graph that is all important, but first let’s look at an version of ThunderStruck falling from 100km. We will need to do this for Phase 2 with a different craft, but let’s look at the maths.

Todd says:
– For mass of the vehicle I used 10kg.
– For the Area of the object in direction of motion (vertically downwards I am assuming for the high speed part of the fall) I calculated the cross sectional area of the cone ie: a circle using the diameter of 600mm as per the current drawings.
– For the Drag Co-efficinet there was a URL on the VUId page that pointed to an aerospace.org page discussing different drag co-coefficients. For a 3D cone the Cd is calculated using a formula that needs a half-vertex angle. From your drawings (cone depth 450mm, cone diameter 600mm) half-vertex angle is 33.7 degrees.

100km release; max speed

max speed for an aircraft released from 100km – from a sounding rocket apogee of 100km

In the graph above, the first part of the flight was a little more difficult than I thought as lots of things are changing as it falls ie: gravity, air density, drag etc but I’ve got there now.

The first model I have done is the 100km drop test. I need to clean up the data below 18000m but the show is well and truly over by then anyway, but I will get it right so the graph is correct (I need to be more accurate with the air density below 18km).

This says a lot. Thanks Todd. This shows that tourist flights to space at just over 100km altitude at apogee will reach a top speed of Mach 3 on their return – that is about 1,050m/s. Then without any further intervention, they will slow to a fall of about 50m/s near the ground. This shows that the Virgin Galactic trick of feathering the craft is all about stability and not speed. There is nothing that will prevent the craft from reaching this speed since there is not enough air to interfere with the acceleration. The “chunky” graph below shows that clearly. Please assume that the peaks to the left in the deceleration part of the graph are correct.

Acceleration from 100km fall and then deceleration

Acceleration from 100km fall and then deceleration

Free Fall Speeds

From the above, you can see the acceleration is flat and continuous until the craft reaches an altitude of 60km and the acceleration starts to slow. It crosses the zero point of a stable speed at about 47km and then begins to decelerate quite rapidly until it reaches 33km altitude. At this point the deceleration slows down and at 20km altitude the deceleration is slowing in the thick air. You may notice that the maximum deceleration is 38m/s/s and since we accelerate at nearly 10m/s/s when we jump from a platform, simply put every 10m/s/s equates (rule of thumb) to 1G. This means that any craft headed straight down will experience a maximum G force of about 4G. Nothing too harsh. Slowing from orbit is very different and we will eventually cover this in future posts about re-entry.

The first thing to notice is that we will never reach Mach 3 from a release at around 45km. We will achieve over Mach 1. There are a few things that we will need to play with to reach the desired Mach 1.5 and we will cover that in a future post as we look at the graph for a drop from 45km and another from 35km.

3D Files and ThunderStruck Phase One

Thunderstruck Half Scale3D Files, Printers, simulations and More

by Robert brand

In the past we used wind tunnels and that was fine for subsonic flights. ThunderStruck does have access to wind tunnels at a number of establishments, but it is unlikely that we will need them. In part because supersonic wind tunnels are rare and because subsonic tests do not translate to supersonic conditions. Why wont we need them? Simply because computer modelling allows us to test most things extremely accurately without  the need for wind tunnels. The first part of the equation is to “make” a 3D model of the airframe and from that the options are extraordinary. Simulations of wind tunnels are just one option. What else can you do with the computer files of your model? well, we are not doing everything possible, but here are a few things:

  • Produced images of the ThunderStruck craft in solid form (we use Solidworks)
  • Rendered the surface to appear metallic
  • Added the ThunderStruck Logo and artwork
  • Animated the control surfaces on the craft
  • Sent it to a TV animator who will use the flight profile to simulate the mission
  • Made 3D models of the craft with a 3D printer.
  • Made a scaled nose cone for the 1/6th size model for demonstrations. Nose cones are immensely hard to create, but so easy with a 3D printer
  • And finally (so far) carried out Mach 2 flight simulations
Thunderstruck Phase One plans and view

Thunderstruck Phase One plans and view 1/2 scale

These simulations show up any problems and thus they have already resulted in small changes to the Phase One craft design. The biggest change will be a longer and more slender nose. You will see why in a moment.

One the right are the original plans from three sides. The software automatically creates the view (top right of image). The 3D files are then produced and it is often that simple. Everything flows from the files. The extension for the files is STL. A printer may break the files up to print an object in two, three or more parts. It depends on the size of object a printer can handle.  we wanted a 22cm model of thunderstruck and that was printed in three parts as it was too wide and two high. The parts were simply joined with acetate. It melts the material slightly and the pieces are then welded together without glue.

The solid image looks like this with a little bit of shadow and a plain surface. A “light source” is placed where needed to create essential shadows for the right feel and look.
Thunderstruck1

The image above has been created to appear to sit on a grey surface. Remove that surface and add a metallic texture and a background image and you get this:

Thunderstruck Phase One Craft in Flight

Thunderstruck Phase One Craft in Flight. Credit Ben Hockley (ThunderStruck) and NASA (clouds and Moon)

The video below shows an animation for the control surfaces. Nothing much to see other than we are working on getting the smaller bits right for the big animations. You can also see our logo on the side so this is a two in one demonstration

Below is a rough picture of the printed 22cm model and the Nose Cone needed for our TV interview on Wednesday with Channel 7 (The Seven Network, Australia). It will be painted. If you look closely you will see the nose cone join and similarly you will see the join on the 3D model.

22cm ThunderStruck Phase One model and the nose cone on the right

22cm ThunderStruck Phase One model and the nose cone on the right

Below is the plan for the nosecone and it is simple to reproduce. Notice the curved area near the base of the nose cone. This is to ease the airflow over the surface and prevent the delamination of the airflow.

Phase One Thunderstruck 1.6 nosecone

Finally we can do simulations. I will explain what you are looking at below in the next post but wow this stuff is impressive. This si not the top end software, but just a basic system and it is more than adequate for our needs:

Airflow_temperature

Most of the work on this page has been provided by Team Member Ben Hockley of Brisbane. I am grateful that we have a person with his skills in the team.

 

The View from 33.33Km Altitude

33.33Km and the Thin Blue Line

UpLift-19 Media and Information

Ever wonder what the view is like 1/3 the way to space. Here is our last high altitude Balloon flight to give you a look. Since it did carry sensors for Project ThunderStruck, it is a big thank you to Clintons Toyota of Campbelltown, NSW, Australia. The balloon was launched from Rankins Springs NSW and the payload weighed 1.5Kg and it was a 800 gram balloon

This is an unedited video and still video images from a GoPro3 Black edition camera of a weather balloon payload area. It climbs to 33.333Km where the balloon bursts and the payload free-falls back for recovery. It was a commercial flight fo Clintons Toyota, Campbelltown, NSW, Australia. They also sponsored a non-commercial payload for Project ThunderStruck – our first test for the Project for a supersonic glider to break Mach 1.5 (1,800kph / 1,120mph)

http://projectthunderstruck.org

The so-called Space Chicken, frame and with the parachute deployed, it reached a top speed of 400kph / 250mph. At the 12 minute 14 second mark on the video (2 hours into the flight) there is a noticeable jarring of the payload and a small pop. This is the balloon exploding. Immediately shredded balloon hits the payload as there is virtually no air to slow it. 2 seconds later, the payload tilts showing the cloud of shredded balloon About 1 minute into the free fall we reached 400kph according to the telemetry. The drag increases at lower altitudes, so the effect of the wind is worse as it descends. It then improves as the air density increases. In the seconds after release you get to glimpse the balloon shreds rocketing into the payload from the explosion and then the cloud of shredded material in the sky. About 10 seconds later there are glimpses of the blue and white parachute not doing much during the fall due to the low air resistance. The cutdown box that is placed above the parachute actually fouls the parachute slightly during the free fall before it becomes effective at slowing the payload. The fouled parachute causes spin at the faster speeds. The video finish with the payload still well above the clouds. This was UpLift-19 by Robert and Jason Brand for Clintons Toyota.

PS, notice that thin blue line in the video and the photos? That is all the atmosphere we have and that is pretty thin near the top. 72 percent of the atmosphere is below the common cruising altitude of commercial airliners (about 10,000 m or 32,800 ft)

Jason and Robert Brand setting up the cameras on UpLift-19

Jason and Robert Brand setting up the cameras on UpLift-19

 Balloon-Burst1-seconds-after-the-event-UpLift-19

Balloon-Burst1-seconds-after-the-event-UpLift-19. Those are the shreds of the balloon.

Balloon Burst3 seconds after the event Note the cloud is getting smaller as the thin air slows it faster. – UpLift-19

Balloon Burst3 seconds after the event Note the cloud is getting smaller as the thin air slows it faster. – UpLift-19

Balloon Burst4 seconds after the event - UpLift-19

Balloon Burst4 seconds after the event – UpLift-19 – yes, that is the sun

Balloon Burst5 seconds after the event - UpLift-19

Balloon Burst5 seconds after the event – UpLift-19

Balloon Burst6 with Parachute in view seconds after the event - UpLift-19

Balloon Burst6 with our blue and white Parachute in view seconds after the event – UpLift-19

Balloon Burst7-Effects of drag are clear after only 24 seconds - UpLift-19

Balloon Burst7-Effects of drag are clear after only 24 seconds – UpLift-19

Balloon Burst8 - Speed has slowed, but drag is greater in the thickening atmosphere - UpLift-19

Balloon Burst8 – Speed has slowed, but drag is greater in the thickening atmosphere – UpLift-19

Note: The images above are from the High Definition Video, not still images. The quality of our camera work has increased dramatically with some improvements to our methodology.

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!: