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
- 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:
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.
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.
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.
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 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:
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: