Calculating ThunderStruck X-2 Speed
Recently we spoke about the spreadsheet that we have created to calculate the speed to be achieved by the ThunderStruck X-2 craft. We took into account a range of figures and that gave us some big design changed to ensure that we could meet the Mach 1.5 speed that we wanted for the experiments on board. Those changes took into account the drag of the vehicle, the angle of the nose cone, the size of the fuselage, gravity at altitude, air density and more. For the sake of the initial calculations we did not bother with the drag of hitting Mach 1 as we believed the air density to be so thin that it would not stop us achieving the speed that we needed.
I am pleased to say that team member Todd Hampson has now incorporated the transonic factors and ongoing supersonic factors into the spreadsheet and I am pleased to say that we were right. There is very little variation in our calculated speed if dropped from 45km altitude. Lower altitudes certainly had issues, but not if dropped from 40km and above. Although we are aiming for 45km using hydrogen, it is possible conditions like potential grass fires my limit us to Hydrogen
The addition factors that we have added to the spreadsheet are:
- Base Drag
- Area Rule
- Transonic Wave Drag
- Supersonic Wave Drag
- Friction Drag
Remember that this spreadsheet is designed to measure an aircraft in a vertical dive into the ground. You can see it slow with thick air to very low speeds. None the less we intend to transition to horizontal flight at below 10km altitude, to the remainder of the graph becomes meaningless at that point.
One of the outputs of the spreadsheet is a set of figures. Below are the figures for 45km altitude release and below that for 40km altitude release. Both heights break Mach 1 sea level equivalent.
Above: Figures showing the results of a 45km release.
Below: Figures showing the results of a 40km release.
Mach 1 at Sea Level and Mach 1 at Altitude
Simply put, altitude does not really change the speed of sound. Temperature does. It is the biggest factor. Because the speed of sound is lower at altitude where the temperature can be as low as -60C, many people feel as if we are cheating if we only break Mach 1 at the altitude that we are traversing. They want to see the speed of sound broken as if we were doing it at sea level. We have provided those calculations here. The chart automatically compensates for the increased effects of the speed of sound at a given altitude by assuming a standard set of temperatures at those altitudes. These vary by time of year and region. We will publish the set of tables that we have used for this in a future post for reference.
For our purposes, the figures used will be accurate enough for the calculations. Why do we know this? Because they do not vary much at the altitudes that we are breaking the sound barrier. The coldest air in our flight will be in the jet stream and is well below 20km altitude.
We intend to give others on-line access to our spreadsheet in the near future, when we are assured all the bugs are ironed out. At this time the spreadsheet looks stable and accurate.
Below is our Velocity Profile showing Max speed in Mach figures. Remember the speed of sound changes with altitude and this is adjusting the Mach figures for the air temperature at each altitude point. The bump near the 15km is the point where the craft decelerates going through the speed of sound. Given its proximity to the ground and the density of air, it is very possible that we will hear a sonic “boom” from this event.
The graph below is the Acceleration Profile in Gee Force. The bump at 15km is showing the additional drag going through the sound barrier to subsonic speeds. there is a similar bump centred at 39.5km, but the air is so thin, it is extremely attenuated and not visible and thus it has little effect.
Below is a graph showing the Velocity vs Time for the first 125 seconds. After this time, the aircraft will level out.
From the top graph – Velocity Profile – if Thunderstruck X-2 continued its dive to the ground, it would hit at Mach 0.27 or 320kph . This is a lot slower than the Mach 1.5 it achieved at 39.5km. Lets hope that the landing will be a lot smoother!