SS1 Flight Parameters
Motor Description
The plan is to fly the SS1 with a long-burn, low-impulse motor in the L class range. The trick will be to keep the weight at lift-off down to a minimum, which of course means building the SS1 as light as possible -- but still rugged enough to survive a high-power flight. This is especially difficult becuase our experience with the 4" test vehicle indicates that a LOT of nose weight will be needed.
Hypertek offers a wide range of L-class motors, and flying this model on a hybrid motor would be a great way to stay true to the original. The low-impulse hybrids will allow us to keep the boost velocity below 200mph. Why would we want that? Remember, the 'fins' on this craft move -- we can't bullet-proof this rocket with tip-to-tip composite reinforcement the way you can (and should) with any other rocket flying on an L motor.
At right is the drawing of the SS1 with a Hypertek fuel grain and a 1685cc 75mm tank. To the right of the SS1 you will see both the 1685cc tank and the 2800cc tank -- I don't believe that tank will ever be needed, but it's nice to know it would fit.
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Flight Simulations
In our typical belt-and-suspenders, anal-retentive way of doing things, we have created a mathematical flight simulation model to help predict the flight characteristics for each motor. It created in Microsoft Excel and is pretty intuitive to use: The different Hypertek motors can be selected via pull-down menu, and the spreadsheet loads in the thrust curve to predict the flight. You can also mess around with other variables like weight, Coefficint of Drag, etc. You can download it [HERE!].
Launch Weight
The target is to keep the total liftoff weight between 40 and 50 pounds. This is an aggressive target that will allow us to use a long-burn, low impulse hybrid motor. If the liftoff weight is just under 50 lbs, we will be able to fly it on a Hypertek L355, which will burn for nearly 9 seconds. If somhow manage to keep the liftoff weight under 35lbs, we could conceivably fly the SS1 on Hypertek L355 225, which would burn for over 13 seconds!
Launch Velocity
One of the main concerns about a low-impulse hybrid is that it does not deliver much 'kick' off the pad. Rocket flights tend to become horizontal if a rocket leaves the guide rail without sufficient velocity. Rockets typically need a minimum of 35 feet per second to generate enough air movement past the fin surfaces before they become effective.
It will be our target to achieve this same minumum velocity - 35 feet per second.
We may need to find a longer launch rail than the 12-footer that I own
We do have the option, since this is a radio-controlled craft, to launch it 35 degrees off of vertical. This will increase our liftoff velocity by reducing the SS1's struggle against gravity. The pilot would just swoop the SS1 gently up into a vertical climb.
Estimated Drag Coefficient
Here is an example of good things coming to those who wait. When I first begean this project, one of my largest concerns was determining the Coefficint of Drag (Cd). Fortunately, John Cipolla has figured this all out for me using computer models and actual wind tunnel test. You can find the incredible documentation of his work testing a scale model of the SpaceShipOne [HERE!]. Work your way all the way down to the bottom and you will find that the wind tunnel testing estimated that the SpaceShipOne Cd = 0.61 -- this is the value I plugged intot the flight simulation model above.
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1:48 scale SpaceShipOne model in John Cipolla's wind tunnel
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Maximum Altitude and Velocity
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At the risk of being redundant, the objective of this flight is to minimize velocity with the longest possible burn motor. At right is a graph that shows the predicted flight statistics for the L355 with an estimated liftoff weight of 50lbs. The maximum velocity is about 169 feet per second and the maximum altitude is about 1100 feet.
There are a range of other higher impulse motors available if the liftoff weight gets away from us.
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The big variable is weight. The table at the right shows that a lower impulse more (L225) with less weight at liftoff (35lbs) still has a maximum velocity of about 160 feet per second but will climb to an altitude of nearly 1500 feet.
This part of the web site will be updated when the SS1 is finally completed and we can determine the actual weight. Stay tuned.
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Glide Weight
One of the drawbacks to using Hypertek hardware is that the spent motor is pretty heavy. So we plan to eject the entire motor mount, along with any nose weight we need to add to make the rocket balanced for the boost. This advantage of this methodology is that we can have one CG appropriate for the boost phase, and a second one for the the glide phase. The glide weight is expected to be around 28 pounds; but once again, the final weight will be posted once the rocket is completed.
Wing Loading
This is a new concept for a rocket builder like me (fortunately there are online resources to help me figure it out). The wing load is basically the ratio of the weight of an airplane to its wing area. Model airplane builders know that scaling down an aircraft creates wing loading issues because the wing area is geometrically proportional to size.
So for instance, a craft with a 16'x12' wing has an wing area of 192 square feet. A craft with a 4'x3' wing has a wing area of 12 square feet. The first craft is four times as large as the second, but the wing area is sixteen times as large. That is basically the ratio we encounter when we compare the SS1 to its full-size cousin.
I plugged the measurements of the SS1 wing into the wing loading calculator found [HERE!] and came up with a wing loading of around 47 to 50 ounces per square foot (using an estimate of 28 to 30 lbs for glide weight). That's double what they recommend for a scale fighter plane and five times the recommended limit for a glider.
On the other hand, the actual SpaceShipOne had a wing load of 49 pounds per square foot. So while this is heavy for an RC craft, if doesn't exceed the limits of the full-up design.
Center of Gravity and Center of Pressure
Aerodynamic stability is determined by the relationship of the Center of Gravity (CG) to the Center of Pressure (CP). CP is indicated on the illustration below as the 'target' symbol. This location is static, based on the design and of the fins and their relative location on the airframe. There are a number of different calculations to determine the CP. The location of the red symbol on the illustration below was calculated from the RockSim model (found [HERE!]) which places CP at 54% of the total distance from the nose tip of the SS1, or 41 inches. The Aerodrag wind tunnel test actually placed the CP at 65%, or 49 inches. I will be using the more conservative of these two predictions for all analysis, comfortable in the knowledge that I am not being unnecessarily aggressive in my margin of error.
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For a design to be stable, CG must be an adequate distance forward of CP — and this distance changes for boost and for glide. Here is what we have already learned about the aerodynamics of this vehicle based on our experimentation with the 4" test mules:
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We know from demonstration where the Center of Gravity (CG) needs to be when the SS1 is in glider mode so it can be airworthy and returned home via remote control. The CG of the glider is shown on the illustration above with the black CG symbol. This is also consistent with the RC pilot rule-of-thumb that the CG should be roughly 1/4 to 1/3 of the length of the wing back from the leading edge.
The green CG symbol is at the location that we proved, through trial and error, stabilizes the rocket while under thrust. As we defined in our analysis of Test Flight One, a marginally stable design will exhibit the tendency to reverse directions when under thrust. The CG at the time this occured was very close to the red CP location.
So we know that we need to balance the rocket with the CG way forward for the boost phase, then move the CG backward for the glider phase. We will accomplish this by ejecting the entire motor mount including the motor and the extra nose weight needed for boost after the SS1 reaches apogee.
The orange CG symbol, by the way, is the center of gravity of the large SS1 without adding any balancing weight or radio control electronics. There will be some additional balancing weight required in order to trim the big pig for the glide phase. The good news is that part of this weight may be a parachute, just in case something catastrophic happens during boost and the SS1 is unable to glide.
INDEX
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