ThunderStruck Progress.

Pajero Jan 2016

Pajero Tracking Vehicle Update

We are on the move after several delays. The proof is in the progress since our last post. We are now talking boosters from our balloon platform to get us to space and we are working on our technology. Balloon test flights are being planned for late January / early February

So lets look at what my son, Jason (13), and I have done and are doing about the tracking vehicle. We will have more, but we are planning on at least having our 4WD SUV ready for the trans-sonic test as soon as we get this approved by CASA – the Australian Civil Aviation Safety Authority.

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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.

2022 Mars Delta-V Requirements

Navigation – Earth to Mars Delta V

by Tim Blaxland – Introduction by Robert Brand

I have not yet introduced you to our Navigation chief Tim Blaxland and I will do that soon enough. Let us just say that he knows his stuff. When I was requested to make Mars the destination of the first shakedown flight of the ion engine equipped ThunderStruck craft in 2022, here was his initial response. This may go over a few heads, but it may be important for you to know that we have the ability to actually do the work required. What we don’t know about building and operating a spacecraft will be firmly supported by the right staff with the right experience and credentials – when the time comes. Until then, please understand that we are a capable team and soon to become a space sector company. I hope that you find this email interesting. I will post some orbital pictures when we have them ready for publication in a week or so..

The importance of this work was to ensure that 2022 provided a window of opportunity to leave for Mars. Here is Tim’s email:

Robert,

These graphs show the arrival, departure and total delta-V requirements for Hohmann-type Earth-Mars transfers. Delta-V is displayed by colour, the horizontal axis is departure date (range Jan 2020 to Feb 2025) and the vertical axis is flight time (range 100 days to 500 days).

I know these aren’t what you were looking for, but they are relatively easy to produce and are moderately interesting. They are based on a simplified calculation method using instantaneous changes in velocity for Earth escape and Mars capture and do not consider things like ion engines which can be used to lower the departure and capture delta-Vs.

At least they give you a useful ballpark approximation of when the available launch windows are.

You’ll notice that there are two lobes to each patch. The lower lobe is the one typically used for conventional chemical rockets because they give a much lower flight time (7-9 months) without too much delta-V penalty. The associated transfer orbit does however have a relatively high eccentricity. They top lobes have longer transfer times but lower eccentricity and I believe they will give us greater opportunity to maximise the use of the ion engines but I need to do more research in this area.

Earth to Mars Delta V:

Arrival delta-V (the cross-hairs are on the minimum for 2022 – 29th July 2022 with a flight time of 321 days)

Arrival delta-V (the cross-hairs are on the minimum for 2022 – 29th July 2022 with a flight time of 321 days)

Departure delta-V (the cross-hairs are on the minimum for 2022 – 17th September 2022 with a flight time of 387 days)

Departure delta-V (the cross-hairs are on the minimum for 2022 – 17th September 2022 with a flight time of 387 days)

Total delta-V (the cross-hairs are on the minimum for 2022 – 28th August 2022 with a flight time of 347 days)

Total delta-V (the cross-hairs are on the minimum for 2022 – 28th August 2022 with a flight time of 347 days)

Tim will be giving me a better breakdown of the navigation profiles, but 2022 is such a long way and we may slip or gain over the years, so it will be little more than an exercise to ensure we understand the time taken with an ion engine and the problems that may arise. I look forward to more detail soon and I will share it with you.