Designing a Rocket Glider using Open Rocket software

[JNUK]

References:
[1] – Super Roc Rocket Gliders by Robert Alway and Peter Always, Research and Development Project for NARAM 42, LINK

In their NARAM-42 report Robert and Peter Always provided background, experimental data and a methodology of designing backwards gliding rockets (Super Roc Rocket Gliders) [1]. In the following brief report I will demonstrate that OpenRoket (OR) allows simulation of such rocket. The simulation results are mainly in agreement with the experimental data.

OpenRocket Model
Based on the description in [1] (Figure 2) an OR model of 40 ½ “ backslider was created

To verify correctness of the model its Barrowman Centre of Pressure (BCP) for different fin sizes was compared to the report (Figure 3). As expected no significant differences were found.
Centre of Lateral Area (CLA) was calculated independently and compared to data in [1] (Figure 3). Again, no disagreement was found.
Changing of the rocket CG was simulated by using OR’s option of the sustained CG override rather than by changing the nose cone/ tail weight as in [1]. Thus the model mass was kept nearly constant in all simulations.

Static Stability Analysis
After the above initial preparation models with different fin sizes were analysed using the Component Analysis power tool available in OR.

The tool performs a static stability analysis of a rocket for a given angle of attack and speed. It was found that the minimum CP distance ( minimum distance from the nose tip to CP) corresponds to an angle of attack less than 90 degree. That minimum CP distance is referred to as Min CP in Fig. A below. Further increase of the angle of attack to 90 degrees leads to slight increase in CP distance (referred as 90 deg Angle of attack CP). It is beyond the aim of this report to analyse mathematics behind this effect.
I noted that 90 deg Angle of attack CP calculated by OP corresponds very closely to a border between regions of “Expected Lawn Dart” and “Expected Backwards glide” observed by Always ( Figure 6, note results key). Approximate border between the two regions in [1] is also shown Fig. A below (yellow line) for references.
After the above step I made a tentative conclusion that OR’s static analysis power tool can be used to establish a range of CG values that could produce the required effect of backwards gliding.

Dynamic Simulation
OR simulation of all flights presented in Table 1, [1] was performed in two wind conditions – 0 m/s and 2 m/s. Main results of the simulation are presented in Table A below. Note results for 0 m/s wind speed are not shown in the table due to their insignificant difference from the presented 2 m/s wind speed data.

Table A.

Fig. A below shows results of the static analysis as well as position of the burnout CG (CG after engine burnout) presented in Table A. Fig. A is to be compared to Figure 6, [1].

Figure A

As it can be seen from Table A, simulated behaviour of the model for given fin size and CP location closely resembles the real flight data. There are only two exceptions – flight #4 and #6. However, CG for these flights is at the border of “backwards gliding” area (see points #4 and #6 in Fig. A). Such borderline condition may explain inaccuracy of the simulations comparing to the real flights.

The following metrics readily available in OR was chosen as indicative of a model behaviour during the descent phase of the flight:
• Angle of attack – angle between the model longitudinal axis and its velocity vector;
• Vertical velocity – vertical part of the velocity vector;
• Vertical orientation (zenith) – angle between the horizon and the model longitudinal axis. 90 deg – zenith, 0 deg – horizon.

It was found that using the above three metrics it is possible to establish whether the desired “backwards glide” occurred or not. For example Fig. B demonstrates “lawn dart” descent (flight #7). After the apogee (approx. 4.7 sec) vertical orientation begins changing from 90 or so degrees to 0 deg (6.2 sec) and further to -90 deg. corresponding to a nose down dive. At the same time the angle of attack reduces to 0 deg and the rocket’s vertical speed increases.

Figure B

A completely different behaviour can be observed on Fig. C corresponding to flight #3 with “backwards glide” descent. After the apogee the model vertical orientation changes to approx. 7 deg and stabilises at that value. This indicates that the rocket does not turn down vertically, but remains in an approximately horizontal position. Note stabilisation of the vertical velocity after approximately 11 seconds.

Figure C

Fig. D presents an interesting simulation results for flight #9. Non-dumped oscillation can be observed. This is due to the burnout CG equal to 90 deg Angle of attack CP.

Figure D

Simulation plots for all test cases in Table A:
• Flight #1
• Flight #2
• Flight #3
• Flight #4
• Flight #5
• Flight #6
• Flight #7
• Flight #8
• Flight #9
• Flight #10

Conclusion
It appears that it is possible to simulate behaviour of a backwards gliding rockets (Super Roc Rocket Gliders) using OpenRocket simulation software. A relationship between CP, CLP and CG of a model yielding the desired gliding behaviour of the model during the descent phase can be easily established using static analysis power tool. Dynamic simulation provided quantitative data for further analysis.

Next step: My initial investigation showed some promising results with regard to using Rocket Optimisation power tool available in OR.

 

[JNUK]

An addition to the post above.

Mathematical Background

[2] - Open Rocket Technical Documentation For OpenRocket version 1.1.6 by Sampo Niskanen, LINK (pdf download, 1.3 MB)

Refer to the OR's technical documentation [2] (pdf download, 1.3 MB) for the software mathematical background.In context of a rocket behaviour in a large angel of attack condition section 3.2 ([2], page 21) provides necessary formulae.

In particular it is important to note that the effect of body lift must not be neglected, especially in a case of a long, slender body ([2], page 24). The normal force exerted on a cylindrical can be calculated using equation 3.26. From 3.26 and 3.19 it can be seen that the normal force coefficient derivatives, CNa, used to calculate CP of cylindrical elements of the rocket depend upon the angle of attack a as sin2a/a.

If CNa calculated using small angle of attach values approximated linearly to 90 degrees (dashed red line), the calculation will yield a total CP equal to CLP. However, as it was mentioned above, such approach is incorrect as it neglects the body lift effect.

 

[JNUK]

A rocket was designed to verify various aspects of a methodology resulting from the analysis described above.

Unlike the models designed by Robert Alway and Peter Always our model did not have a vent port in the top section of the body tube to assist transition to a high angle of attack (AoA) state. Two symmetrical ports were cut approximately at the CG location along the body tube. It was a deliberate design approach aiming to eliminate any influence of the motor ejection charge upon pitch of the model, thus allowing a more accurate evaluation of OR's predictions (at least we hopped so). Also, it allowed motors with any delays to be used without affecting the model apogee.

In general three design approaches can be used:

• Fixed CP: For a given aerodynamic configuration () of a model location of its CG is designed to satisfy conditions necessary for the back gliding effect to appear;
• Fixed CG: For a given mass distribution and body dimensions of CP is adjusted to allow the back gliding effect;
• Mixed approach: Iterative combination of the above two methods.

For purposes of this project we used the first approach. The fin shape/size and the length of the body were unchangeable elements. Design very similar to the Estes's Comanche-3 upper stage was used. Original shape and dimensions of the fin set are retained without changes. Nose cone and the body tube length were change to utilise components available in our scrap box.

The complete OpenRocket design file and a detailed specification can be found here.

Fixed CP Design Methodology

The methodology is descried as series of consecutive steps. However, it has to be noted that the process is in fact iterative and may require several iteration before a satisfactory result can be archived.
Step 1 - Verify CP location

Exact mass of the rocket and its distribution are not important for this step. Thus, the rocket model can be designed in OR without paying attention to materials and mass of elements. The important aspects are:

• Shape and dimensions of the the nose cone;
• Dimensions of the body tube;
• Shape, dimensions and position of the fin set.

Location of the model CP vs its AoA is analysed using the Component Analysis power tool available in OR. The graph below shows the relationship.

From the above graph it can be seen that when AoA changes from 0 to 90 degrees, CP changes between approximately 750 mm and 595 mm measuring from the nose tip.

Step 2 - Verify take-off stability margin

It is important to model mass of all elements as accurately as possible for this this step. Also the assessment is to be carried out for all motors intended to be used. Table (LINK) summarises the results.

Step 3 - Verify CG on the motor burn-out

Position of the CG after the motor burn-out can be obtained from the simulation data. Alternatively a mass element can be introduced to simulate an empty motor casing. The picture below illustrates this approach.

The model burn-out CG=616 mm. From Fig. AA it can be seen that CG remains aft of CP for AoA up to 105 degrees. Therefore, conditions required for back sliding are satisfied.

It is quite possible that initially CG may not fall into the required CP "brackets". In that case CG balancing is necessary. For the described model it was achieved by the following:

• Reducing the nose cone weight. From several available nose cones the lightest made of the less dense balsa was selected.
• Increasing weight of fins. Opposite to the nose cone denser, heavier balsa was used.
• Increasing weight of the motor mount. No additional mass elements were added. The weight increase was achieved by using denser cardboard, increasing length of the motor block and two centring rings.

Step 4 - Dynamic simulation

Dynamic simulation is performed with a required motor(s). Table below shows a simulation summary for 2 m/s wind speed and 10% turbulence intensity.

The following graphs present simulation results for Estes B6-4 motor.

Figure BB Vertical Motion
Figure CC Total Motion
Figure DD Flight Side Profile

The Plot below is the most interesting of all. It illustrates the relationship between CP, CG, vertical orientation, angle of attack and velocities (or rather speed) during the flight.

Flight Test

The test flights were performed in moderate wind conditions with the maximum wind speed approaching 6...7 m/s. However, at the launch pad location the wind speed was somewhat lower providing safe launch conditions.

The model made three successful flights. Estes B6 motors were used (2x B6-4 and 1x B6-6). In all three flights the backward gliding was observed. The rocket glided with slightly elevated nose, which was consistent with the predictions. Despite the wind blowing in one direction the glide path was not straight , but somewhat spiral. One of the flights was timed with a stop watch. Its duration was 20 sec. The other two flight were not timed, but were at the same scale. The time was consistent with the predicted flight duration.

It is interesting to not that no significant roll was observed during the glide. Slight rolling left-right was present though. Perhaps +- 10 degrees.

One of the landings was a hard one resulting in two broken fins. This is an unfortunate specific of the type. More attention to fins is required.

The forth flight (Estes B4-2) was performed in conditions of changing and strengthening wind and resulted in a lawn dart and a destruction of the nose cove and the top section of the body.

Post Flight Analysis

A series of simulations was performed to establish a cause of the crash. The only hypothesises was an influence of the wind turbulence during the moment of transition to the glide at the apogee. A simulation was set with the Wind speed 6 m/s and Wind Turbulence 25%. The simulation was replicated 100 times (using Cntr+C - Cntr+V) on the OR's Flight Simulation tab. Then the set of 100 simulation was selected and run 10 times providing 1000 independent results.

None of the simulation indicated any issues during the take-off phase. However, a lawn dart happened in 2.5% of the simulations. The plot below illustrates such behaviour.

A significant wind turbulence prevents the state of a high AoA from occurring at the right moment. A possible solution to the issue is to find a way to move ether CG backwards or CP significantly forward.

Conclusion

With a degree of confidence I can say that a reasonably simple yet robust methodology utilising OR software has been created. I am very please with the results.

 

[FastCargo]

I thought this was a very interesting analysis and testing used for the design. A few questions:

1) Do you consider buildup of ejection material in repeated launches to cause problems with CG shifting to go into 'glide' mode? I would imagine after a while the CG would never be far enough back to help get the AOA you need.
2) Based on what I'm reading, this kind of rocket as built is not a good candidate for windy days, since it would tend to not want to generate a high AOA at the right time...would I be correct in assuming this?
3) I'm intriged by the idea of a CG shift at the ejection event, sort of 'forcing' a high AOA condition to avoid the 'lawn dart' event...I would assume something like an old Estes Scout method of CG shift would work?
4) Finally, how tolerant would the design be to different engines (ie does a used A8-3 casing weight about the same as a used C6-5 casing)?

FC

 

[JNUK]

I thought this was a very interesting analysis and testing used for the design.

FC

Thank you very much for your interest and questions.

1) Do you consider buildup of ejection material in repeated launches to cause problems with CG shifting to go into 'glide' mode? I would imagine after a while the CG would never be far enough back to help get the AOA you need.

FC

Interesting thought. No, I did not consider that. For my particular model it is not that much an issue. On the photo you can see that the ejection vent ports are in the middle (top of the white middle section, above the launch lag. The second port is on the opposite side). This is approximately there CG is. So, any additional mass due to the ejection material will not change CG much.
In case of ejection through a port near the nose cone, I would think CG could possibly move forward a bit, but I don't know by how much.

2) Based on what I'm reading, this kind of rocket as built is not a good candidate for windy days, since it would tend to not want to generate a high AOA at the right time...would I be correct in assuming this?
FC

Absolutely correct. I've just noticed that in my last post above one of the graphs is not displayed. Or may be it's just my browser playing. The graph is below or alternately here is the LINK



Backsliding has an inherent issue. A long rocket requires a significant static stability margin to remain stable during the take-off. The stronger the wind, the further fore CG has to be placed. However, the further for the take-off CG moves, the further fore the burn-out CG moves as well. At some point it'll get over any possible CP locations, thus negating the backward sliding effect.

There is a way to offset the above effect a little bit. The take off stability can be improved not only by moving CG forward, but also by increasing the off-rod speed as tan of AoA at that moment = wind speed/off-rod speed (of course I assume both are perpendicular to each other). However, for cases of A, B or C motors this does not work very well. I would assume that some kind of a booster (e.g. on D motor) may improve the situation.

3) I'm intriged by the idea of a CG shift at the ejection event, sort of 'forcing' a high AOA condition to avoid the 'lawn dart' event...I would assume something like an old Estes Scout method of CG shift would work?

FC

I though about that. In fact the discussed model was design with the motor assembly moving backwards at the ejection by about 25 mm. It didn't work very well because I'd misjudged friction between parts.
However, it is not the best way in case of low power models. The problem is that an empty motor casing is relatively light comparing to the rest of the body and it is relatively close to CG. Thus it aft displacement mast be significant to be able to shift the total CG significantly.
The better way would be adding an additional weight as close as possible to the nose cone to provide stability during the take-off, and then erecting it. The longer the rocket, the less weight will be needed. For example several grams of a tracing powder could be enough. The key is to keep it at the top during the take off.

4) Finally, how tolerant would the design be to different engines (ie does a used A8-3 casing weight about the same as a used C6-5 casing)?
FC

The empty casing mass is, from my measurements, about 10...12 grams. Such difference doesn't really change anything in terms of transition to the glide. But a lighter motor will make the rocket potentially more stable during its take-off. In the table (LINK) I analysed how much CG moves for different motors.

This particular model can be flown on A motors. However, I suspect that the may be an issue with altitude. On A motor the apogee would be about 50 meters. The rocket needs about 30...35 meters to get into a stable gliding state. It leaves only 15..20 or so meters for the actual gliding.

 

[JNUK]

3) I'm intriged by the idea of a CG shift at the ejection event, sort of 'forcing' a high AOA condition to avoid the 'lawn dart' event...I would assume something like an old Estes Scout method of CG shift would work?
FC

I've failed to mention another possibility. Instead of shifting CG backwards, CP can be moved forward. I'm currently rebuilding the model and planning to try the idea. I'm adding a small and thin (0.15mm) flexible plastic fin just below the nose cone. During the boost phase it will be wrapped around the body causing no abstraction to the air flow. On ejection it will be released forcing CP to move fore a bit.