Curiosity Style Egg Drop Lander

[Brotoro]

Sounds more like the landing profile of the

instead of the

Only if you give me lots of airbags to play with. But I thought the rules were to set the egg down naked.

[Nuke]

id go with a small lipo battery over a cap bank due to size constraints (if you want lots of capacitance, you are going to need a large bank). some of them brushless motors eat power like it was nothing.

[technicalfool]

Micro hybrid motors based on cardboard or latex fuel and NOX creamer bulbs as the oxidizer have apparently been known to reach a high D to E class. More than enough for four of them to hold an egg up for quite a while.

Still, you'll have a problem with throttling, you'll probably want some kind of accelerometer/gyro board in addition to a microcontroller (the Arduino is a good hobbyist microcontroller board), and you'll need to be able to ignite your engines simultaneously in mid air.

A very ambitious project. I hope it goes well for you.

Edited July 2, 2014 by technicalfool

[Ralathon]

Hypergolic fuels would make the ignition problem a lot easier. You could try hydrogen peroxide decomposition via a platinum catalyst as K^2 mentioned earlier.

[christheman200]

You could name it Dragon's Egg.

That is ingenious!

K2, I know a number of people who have worked with 400+psi systems before so I'm hoping that they can give me some help on that issue. If you didn't know, your average cheap 2 litre pop bottle, with a bit of splicing and reinforcement, can hold up to 200psi.

There will initially be a parachute to slow and guide the descent, which would greatly reduce the impact speed. If dropping the rocket from the parachute at 10 meters up, there's only 14m/s potential acceleration there, and some of that is lost to drag. It would already be going pretty slow. I'll have just over 30m/s of delta-v to pull the maneuver off from there.

Are there any options for relative altitude measurement that can sense from ~15 meters, even if they aren't commercial? I've heard of some quadcopters using a wireless link to a computer to be controlled, perhaps external sensors could sense the rocket's height and work from there?

I'm still considering high delta-v options, but I don't have a university aerospace department on my side... yet. I'd rather make sure that an option like a water-rocket isn't possible before moving onto something a bit more complicated.

[Idobox]

A simpler way to do this is to use a single unthrottled water rocket and perform a suicide burn.

Basically, you need to know exactly how much thrust your rocket will provide for how long, and start it at exactly the right moment for you egg to reach altitude zero with speed zero.

Water rockets are not the best option for that, and you'd be better off with something that has less thrust for longer (less precision required), also I'm not sure an egg could survive that kind of acceleration. Maybe using a tiny nozzle could help. A solid rocket could do it if you could reliably time the start-up.

Of course, you need to keep your egg away from the exhaust. The easiest way to do it would be to keep the egg off axis, and have a counterweight on the other side to keep things balanced.

If you really want to use proper throttle, an option is to use a valve at the exhaust of a solid rocket. The smaller the aperture, the higher the inside pressure, the higher the temperature and burn rate. Because there is a positive feedback, you need a lot of precision. Also, it can easily explode. Finally, I have no idea how heavy and expensive a valve able to survive that would be.

[technicalfool]

If you really want to use proper throttle, an option is to use a valve at the exhaust of a solid rocket. The smaller the aperture, the higher the inside pressure, the higher the temperature and burn rate. Because there is a positive feedback, you need a lot of precision. Also, it can easily explode. Finally, I have no idea how heavy and expensive a valve able to survive that would be.

And that's why, if you want a throttlable engine that isn't liquid fuelled and isn't a pop bottle water rocket, you go hybrid. The only thing that'll happen if you slam the NOX valve shut will be that the engine flames out. Close the exhaust on a solid, and you've basically built a pipe bomb.

It's also a lot more stable and much more easy for an amateur to attempt than trying your hand at cryogenic liquid fuels or platinum-catalyst monopropellants. Plus room for experimenting with the optimum fuel type and grain shape. Latex? Paper? Acrylic? Star-shape core? Cylindrical? Other?

Though I think regardless of how the OP means to do this, it's going to require some quite detailed engineering thought. Any of the resident Real Rocket Scientists^TM want to give this guy a hand (if they haven't already)?

[astropapi1]

If I had to do this while keeping it cheap, simple, and still using rockets, I'd go for a Spirit/Opportunity approach instead of the skycrane.

Basically, use a chute to leep it slow during descent, then cut the chute about 10m above the ground, and activate 4 small SRBs angled outwards at the right time just so the egg reaches 0 velocity at 0 altitude. The egg separates and the skycrane accelerates upward, leaving the (hopefully) intact egg in the ground.

Since it's a suicide burn, you wouldn't really need the throttle control and could use simpler rockets than Hybrids, like sugar or water ones; Your landing "computer" would be made of a laser/radar altimeter, one of those mini arduino thigies, and precise ignitors for the rockets.

I'm not an aerospace engineer (yet...), but I think that should be work. After all, Russia's PTK NP will land using SRBs.

[Duxwing]

This problem sounds like an engineering nightmare...

Try keeping things simple. 400psi water rockets are best because they involve no fire and little possible shrapnel. Use store-bought parts to keep things simple. Below are my recommended construction steps:

1 - Buy a cheap micro-controller that can activate a solenoid valve, the parachute, and a spark-gap at hand-calculated times.

2 - Buy a power supply sufficient for the micro-controller and its tasks; e.g., a capacitor.

3 - Connect your power supply to your micro-controller and your micro-controller to your solenoid valve.

4 - Connect your solenoid valve to your pressure vessel.

5 - Buy some Gorilla Glue and some PVC pipe the diameter of your solenoid.

6 - Gorilla Glue the PVC pipe to the solenoid.

7 - Buy three household funnels.

8 - With the PVC pointing downward, drill three holes into the PVC holes at forty-five degree angles to the ground at one-hundred-twenty degree angles to each other; i.e., they form an equilateral triangle when viewed from above.

9 - Buy a PVC pipe-cap.

10 - Gorilla glue the pipe-cap to the end of the pipe, making the funnels the water's only outlets.

11 - Buy some Styrofoam.

12 - So gorilla glue the Styrofoam to the pipe-cap as to allow the egg, when horizontal, to touch the ground before the nozzles.

13 - Buy some Scotch Tape.

14 - Scotch Tape each egg to the Styrofoam.

15 - Attach your parachute to your pressure vessel and put your spark-gap on your tape.

16 - At T = 0 , the contraption will drop via its parachute until T = x, when it will be near the ground. At T = x, the micro-controller cuts the parachute and opens the solenoid valve, causing water to rush through the nozzles, soft-landing the egg at T = y. At T = y, the spark gap will melt the tape, freeing the egg and so increasing the sky-crane's TWR as to cause the sky-crane to fly away, leaving the egg unharmed.

-Duxwing

[christheman200]

I like your simple approach, Duxwing. I never thought of using a spark gap to sever the connection with the egg, however I have my doubts about the strength of the tape.

I feel that the are too many variables for it to be possible to pull off a suicide burn landing, but it is simpler so I'll look into it.

[christheman200]

Using NASA's terminal velocity indicator, with a parachute 6 feet in diameter and the coefficient of drag set to 1.3, at a weight of 10.5 pounds, the terminal velocity is indicated to be 4.5 meters per second.

That is quite a large parachute, but it certainly would take away a large portion of work for the rockets, and give a lot of extra time to react before landing. If the rocket were released from the parachute at an altitude of 10 meters, there would be a potential change in velocity of 14m/s plus the already existent 4.5m/s. That adds up to 18.5m/s, well within the delta-v budget of ~30m/s. The fall would take 1.429 seconds without any forces acting on the rocket.

[K^2]

You could try hydrogen peroxide decomposition via a platinum catalyst as K^2 mentioned earlier.

Platinum's expensive. You can make a good catalyst for H2O2 from potassium permanganate. One of the products of heat decomposition of it is a strong catalyst for hydrogen peroxide decomposition.

K2, I know a number of people who have worked with 400+psi systems before so I'm hoping that they can give me some help on that issue. If you didn't know, your average cheap 2 litre pop bottle, with a bit of splicing and reinforcement, can hold up to 200psi.

Soda bottles are very unreliable. The 2L ones can usually hold 4-5atm even without reinforcement, but some will burst at under 2. If you think you know what you're doing, go for it. Just be careful. And I would consider using something a bit more reliable than a soda bottle.

Are there any options for relative altitude measurement that can sense from ~15 meters, even if they aren't commercial? I've heard of some quadcopters using a wireless link to a computer to be controlled, perhaps external sensors could sense the rocket's height and work from there?

There are a lot of options, of course. The limitations are price, weight, and power consumption vs range and precision. I'm not aware of any son/rad/lidars that would give you significantly better range at acceptable reliability that don't come with a price tag and weight of a commercial aircraft ground radar. Doesn't mean they don't exist, of course. And yes, having a base unit does open up some additional possibilities. If base station is located a bit to the side, for example, you can turn a simple radio receiver into a VOR receiver. Building a mini VOR station is also not that hard. But it's a project all in itself.

There are two more cheap options that you can throw in to get a rough estimate on your altitude. Maybe use it to disconnect the parachute and kick on the engines at low power a bit early, and then throttle up as you get within sonar's range. If you drop your velocity to 15m/s or less with a chute, and come in gently, you should have enough altitude/thrust reserves to fix any problems.

So if you don't mind some work on extra wiring and coding (consider ordering a custom circuit board; it's not that expensive) you should probably throw in a cheap GPS receiver and a good pressure sensor. If you calibrate pressure sensor prior to launch and manage to make a good static port, with a good sensor you can get surprisingly accurate altitude readings. If you get two pressure sensors and a pitot tube, you can get air speed as well. Vertical air speed is a good indicator of your true vertical speed. Similarly, GPS can put you within a few meters on altitude. Not as reliable as pressure sensor, but you can get very good velocity data from it, and maybe you can come up with other uses for it. Naturally, you want to combine readings from both and pass them through your filter. (Like I said, I strongly recommend Kalman filter for this.) Even if GPS readings are way worse than pressure data, with the right filter, even a very bad reading from a secondary instrument can help you reduce error on your primary.

With pressure sensor backed up by GPS, I think you can get to the parachute release and kick on the engines within ±5m. Then do corrections once you are within sonar range, and final corrections in IR range for a soft touchdown.

That kind of leaves stability as your weakest link. Don't go cheap on accelerometers. Make sure you have enough of them to get good six-axis readings. Consider spending a bit extra on optical gyros. (Ring Laser or Fiber Optic) These things are crazy precise for measuring angular velocity. Also bulkier and significantly pricier.

The rest is up to MCU, coding, and reliability of any mechanical parts. I guess, that's mostly going to be your pressure system and valve control. Unfortunately, mechanical parts are where I'm pretty much useless in terms of good advice. I don't have any better ideas than bolting micro servos on to valves, and I'm not sure that's fast/reliable/precise enough. If you'll want any advice on the code once you're working on it, though, I'll be happy to help out.

Edited July 2, 2014 by K^2

[christheman200]

I'll greatly accept any help you can give me with the code once I get to that stage.

I'll be using a composite pressure tank of some kind, and with enough research and testing this method should be safe.

I had the idea to use a 50 meter tall board with painted black and white horizontal stripes, and an onboard camera to measure the number of stripes passing by per second. Filtering with gyroscopes to cancel out any rotational impact on the velocity would give you as much accuracy as you need. It seems ridiculous but it might be the best option.

I've just purchased a copy of Matlab so that I can start learning it's environment and start modelling some of the aspects of the craft. My father also asked one of his colleagues from university if I could get a tour of our local university's engineering/aerospace divisions and if he could find me a mentor in the aerospace division.

The rocket will be called DragonEgg, and if I create my own valves they will be named Python.

[K^2]

Say you get a 60 fps camera and drop it at 10m/s. If your markings are less than 20cm apart, they'll start to blur together. And that's assuming a stable enough fall that no vibration or tilting cause problems. And then you have to process the image, which is going to be tough to do with time constraints using an MCU. It's an out of the box idea, but I don't think it's workable in this particular case.

Now, if you have an external high speed camera connected to a decent computer that will radio lander's altitude in, that could really work. Nobody said you couldn't use some telemetry, right? Might not even need the board with markings if you calibrate it in advance.

[Creature]

I don't want to discourage but 50 meters is pretty high. You're not gonna find a board like that. In fact I was gonna ask where you're planning to drop it from? You need something like a crane or a tower of some sort. I just checked that where I live the highest water towers are 55 meters tall. So imagine a wooden board the length of a water tower or a large factory pipe. That's 50 meters.

[Nuke]

you could probibly reinforce a soda bottle with epoxy and fiberglass/carbon fiber. the bottles are thickest towards the base and also around the opening, but paper thin around the cylindrical part. wrap from under the ridge beneath the cap to the tail end should be sufficient to contain pressure.

i think the typical way you lay out fiber composites is to lay down a layer of epoxy and then lay down a fiber mat (for a bottle you might want to wrap the bottle, overlapping once, and alternate your seams). repeat while rotating each additional layer 30 degrees from the previous one. give it a final macro coat of epoxy. you then vacuum seal the finished part in a plastic bag and you can use heating pads to accelerate the curing time.

[christheman200]

I'll likely use telemetry.

I'm looking into the fiber composite bottles.

[christheman200]

A few days of hard thought has been put into how I should approach the DragonEgg project.

I have decided to take a marketing-oriented approach to the development of the final product. This means that I will be advertising the concept where applicable in order to gain funding and/or partners.

Lander development will continue as usual, however more focus will be placed on finding support.

Appended is the first draft of a poster to be circulated among local universities. It is not quite what I would like it to be, and the wording must be redone, but it is just a first draft.

What recommendations do you have that I can implement in the next iteration?

Edited July 5, 2014 by christheman200

[Duxwing]

@chris

Thanks! Further notes:

1 - When you defined the challenge, you mentioned not autonomy: need the lander now be autonomous? If it need not, then remove the weighty control systems and remotely transmit their commands to the lander.

2 - Instead of using a fifty-meter board with black-and-white stripes, use fifty meters of string with black-and-white marks at each foot.

3 - Better yet, save materials and headache by calculating how much extra 'oomph' a lander built for a fifty meter drop would have at a more-practical height--e.g., six meters--and measure that extra 'oomph' during tests.

4 - Reduce propellant mass by calculating how quickly the egg can safely hit the ground, making your parachute decelerate the egg to that speed, and setting your rocket to simply maintain that speed during the final descent.

More on note four:

Maintaining descent speed requires some mass of propellant, which we must calculate. Please check my following estimate because it seems flawed.

Let the falling assembly mass 1 kilogram.

Weight = kilograms * ten meters per second

Therefore: the egg weighs 10 newtons

Let Thrust equal Weight

Thrust = mass flow rate * Vex

Therefore: 10N = mass flow rate * Vex

Vex = Isp * g

Isp = 65.1 sec

Therefore Vex = 651 m/s

Therefore: 10N = mass flow rate * 651 m/s

Therefore: mass flow rate = .015kg/s

Propellant mass = mass flow rate * burn time

Burn time = descent speed * descent length

Let descent speed = 1m/s and descent length = 2m

Therefore: propellant mass = .015 * 1 * 2 = .030kg

I therefore estimate that you will need thirty grams of water for your final descent--slightly more if you want the sky-crane to lift-away.

-Duxwing

[christheman200]

Duxwing,

it seems like autonomous landing is not necessary. Every gram saved is a larger tolerance for error.

From a single internet source, I shall assume that the egg can withstand 3.75 pounds of force, or 16.7 Newtons. I will need to test for this myself.

The first problem with your calculations is that you are not including the changing mass of the rocket over time.

The second major problem is that the exhaust velocity of the water is around 25m/s.

To provide a force of 10.78 Newtons with a weight of 1.1kg:

10.78 = m-dot * 25 m/s

m-dot must equal 0.43kg per second

To provide a force of 47 Newtons with a weight of 4.8kg:

47 = m-dot * 25 m/s

m-dot must equal 1.88kg per second

To solve this you need to do some integration.

If ANYONE knows how to integrate this problem, please do so and provide some basic information on how it was derived. I'm still learning the prerequisites for calculus.

Using simple geometry, the exit nozzle of a water rocket at 400psi with a weight of 4.8kg, providing a force of 47 Newtons must have a radius of 0.489cm.

[Duxwing]

Duxwing,

it seems like autonomous landing is not necessary. Every gram saved is a larger tolerance for error.

From a single internet source, I shall assume that the egg can withstand 3.75 pounds of force, or 16.7 Newtons. I will need to test for this myself.

The first problem with your calculations is that you are not including the changing mass of the rocket over time.

The second major problem is that the exhaust velocity of the water is around 25m/s.

1 - Good

2 - Written like a good scientist.

3 - D'oh! Perhaps we should computationally model the system.

4 - D'oh!

To provide a force of 10.78 Newtons with a weight of 1.1kg:

Where did you get 1.1kg? I assumed that the assembly massed 1kg. Also, a rule of thumb for rocket design: always round to two sigma. A corollary: all 'good' numbers round down, whereas all 'bad' numbers round up. I follow these rules because the efficiency of failures is banal and because they have taken a lander to Laythe.

10.78 = m-dot * 25 m/s

m-dot must equal 0.43kg per second

For example, following these rules (with my former assumptions) yields:

10N = m-dot * 25m/s

m-dot = 0.40kg/s

To provide a force of 47 Newtons with a weight of 4.8kg:

47 = m-dot * 25 m/s

m-dot must equal 1.88kg per second

I'm confused: where are you getting these numbers?

To solve this you need to do some integration.

If ANYONE knows how to integrate this problem, please do so and provide some basic information on how it was derived. I'm still learning the prerequisites for calculus.

I just learned calculus last year! Before we begin integrating, we must solve a thorny technical problem. because I just realized that thrust and mass independently vary with time: the air pushing the water out the nozzles expands with time, decreasing its own pressure. We can fix thrust by using a Super-Soaker-inspired constant-pressure system--essentially a bladder tank--because the bladder will maintain constant internal pressure by so contracting as the water exits. The thrust-to-weight ratio of the skycrane-egg assembly (SEA) therefore will increase with time just like those of our rockets do in KSP. Without throttling, the SEA therefore will accelerate upward upon rocket... ignition?

Fortunately, we can exploit this upward acceleration! As the rockets... burn? so the SEA will decelerate until momentarily hovering. Intuitively, the time when the SEA hovers should always be the same; therefore, igniting the rockets at just the right time could cause the SEA to hover at a height from which the egg could safely fall.

The greatest height at which the egg could safely fall varies with the greatest force the egg can endure, which varies with the momentum of the egg just-before impact and in how much time that momentum is lost. We have two variables to consider because we know not how quickly the momentum will be lost. I will assume 0.01 seconds (fifty times worse than a car crash) for the sake of the calculation and safety margin.

mv = Ft

v = Ft/m

v = 16.7 * 0.01 / .070

v = ~1.2m/s

Vf^2 = Vi^2 + 2ad

Vi is the initial velocity, which we will let equal 1 m/s

a is acceleration, which we will let equal 10m/s^2

d is displacement, wherefore we solve

Vf is the final velocity, which we will let equal v from the previous calculation

Therefore: 1.2^2 = 1^2 + 2*10*d

1.5 = 1 + 20d

0.5 = 20d

d = .025

That distance is 2.5 centimeters, making-tiny our margin-for-error: can you do it?

Using simple geometry, the exit nozzle of a water rocket at 400psi with a weight of 4.8kg, providing a force of 47 Newtons must have a radius of 0.489cm.

Excellent. So cut the funnels as to make their diameter that measurement.

-Duxwing

[The Jedi Master]

I can't really help, but I am looking forward to seeing this in action!

[Creature]

With a problem like this integration is essentially just adding a tiny step to the equation. It's usually taught so that when you're integrating an area under a curve, you divide it into thin rectangular slices starting from y=0 up to the curve and then adding all those bars together.

Now since you have only a short time interval, you can simulate it with excel without needing any integration at all. What you do is you plug in the parameters like mass flow,total mass, thrust, speed etc. at t=0 into excel. Then you add a timestep, like 0,05 seconds and now since you know what the mass flow out is you know the new total mass at t=0+0,05 seconds and you can calulate the the new acceleration, new speed, thrust and whatever you want based on the new parameters. Then just keep adding the timesteps for a nice acceleration curve, variable thrust and even dropping the egg as an additional reduction in mass.

This takes some excel skills but you're gonna need them in any case later in life with 100% certainty so it's not a wasted effort. But it's also a lot easier than learning integration with multiple variables. The downside is that it's not as accurate mathematically but I'm pretty sure that the inconsistencies in the actual craft will generate more error than the approximation from the steps (if you keep the steps small enough).

I still would want to point out one thing with your dropping altitude. Since you're coming down with a parachute, when it's open the craft is descending at terminal velocity so it makes no difference whether you drop it from a 20 or 50 meter tower or from an airplane. So when designing you don't need to get to 50 meters to test anything, just make sure the chute is fully deployed and the craft has reached terminal velocity when doing tests. In fact you only need to test the terminal velocity with the parachute deployed, then afterwards calculate how high you need to drop the craft from to achieve the same speed and further on just test by dropping it from that altitude above the parachute cutoff point.

For example if your cutoff point is 5 meters from the ground and terminal velocity is 5 m/s with the chute, then you only need to drop it from roughly 6 meters or so to simulate the cutoff speed and altitude.

Also what I'm thinking is that the safest bet would be to use a analog altimeter (strings with weights attached to them) as someone already suggested. Use 4 and when the weights hit the ground, they release the switch for the landing rocket.

As Duxwing calculated, you have very small margin of error to drop the egg. What I'd suggest is you use the water rocket only to touch down, have 4 landing legs with shock absorbers and a switch to sense when the full weight of the rocket is on the legs. This switch releases the egg from precalculated drop height (1-2 centimeters off the ground when landed) and simultaneously ignites solid rocket boosters that lift the craft off the ground. These are available commercially but I don't know about your contry's legislation, at least in my nanny-state they're very highly regulated and you need a license. But they are powerful and light weight.

In ideal situation you'd have the lander cut the chute, come down in freefall (remember aerodynamics!), weights hit the ground and ignite water rocket at exactly known altitude, craft lands (can be a bit bumpy too!), switch drops the egg and ignites the solids and the DragonEgg is laid in a puff of smoke, steam and fire while the lander soars off and possibly gets all tangled up in the still-airborne parachute and catches fire.

[christheman200]

I used 1.1 kg to account for the rocket with 100 grams of water left, and a dry mass of 1kg.

The 47 Newtons of force calculation came from a rocket mass of 4.8kg, since I need a mass fraction of 3.8, meaning 1kg dry mass and 3.8kg of water.

4.8kg x 9.8m/s = 47 Newtons

I like the idea of using a bladder tank, but I don't think using one is possible at 400psi. Carbon fiber seems to be the way to go.

I know NASA does their tank pressure testing by measuring the heat and size of the tank, as well as other variables instead of swelling them up until they explode. I need to re-read over some of my tank design books.

I didn't consider the drop in pressure as water leaves the tank. This will throw my calculations off a lot. Perhaps a compressed CO2 tank can be injected into the system to maintain a pressure of 400psi.

Having the rocket slow down at just the right time is the idea.

Fall testing the egg is my next priority, and will give me the ability to truly define the characteristics of the rocket's flight.

The idea is to touch the egg to the ground, and then let go and fly away. In this case we don't have much margin for error if the rocket fails, however if the rocket performs to expectations the egg should survive intact.

Creature,

I'll give your excel integration a try. I have no experience in Excel, but it still seems like a lot less work than teaching myself the math behind it. Learning matrices, complex numbers, and Matlab this week have already put a good strain on my brain.

I've realized your point on drop height. I just think that if I can find a building to drop it from it might seem a lot more awesome than dropping from a few feet. It also gives a longer time for the chute to open in-case their is a malfunction.

The analog altimeter seems like a smart idea. As mentioned above the idea isn't to land, but touch the egg directly to the ground.

Here's a record of my initiatives in the past few days:

I made a sheet with equations that defined the characteristics of the rocket, which I now have to redo because of the change in pressure over time.

I made a rough draft of a poster to send to academic institutions in my area. I will further this either today or in the coming days.

I've gone through all of imaginary and complex numbers, matrices, and have started linear algebra on Khan Academy.

I've made a list of egg mass vs. egg major and minor axes. By combining this with drop test data I hope to seek new incites into the mechanics of egg dropping.

[Duxwing]

With a problem like this integration is essentially just adding a tiny step to the equation. It's usually taught so that when you're integrating an area under a curve, you divide it into thin rectangular slices starting from y=0 up to the curve and then adding all those bars together.

Now since you have only a short time interval, you can simulate it with excel without needing any integration at all. What you do is you plug in the parameters like mass flow,total mass, thrust, speed etc. at t=0 into excel. Then you add a timestep, like 0,05 seconds and now since you know what the mass flow out is you know the new total mass at t=0+0,05 seconds and you can calulate the the new acceleration, new speed, thrust and whatever you want based on the new parameters. Then just keep adding the timesteps for a nice acceleration curve, variable thrust and even dropping the egg as an additional reduction in mass.

This takes some excel skills but you're gonna need them in any case later in life with 100% certainty so it's not a wasted effort. But it's also a lot easier than learning integration with multiple variables. The downside is that it's not as accurate mathematically but I'm pretty sure that the inconsistencies in the actual craft will generate more error than the approximation from the steps (if you keep the steps small enough).

For extra accuracy, use trapezoids instead of rectangles. For simplicity, average the first and last values and multiply the product by time.

I still would want to point out one thing with your dropping altitude. Since you're coming down with a parachute, when it's open the craft is descending at terminal velocity so it makes no difference whether you drop it from a 20 or 50 meter tower or from an airplane. So when designing you don't need to get to 50 meters to test anything, just make sure the chute is fully deployed and the craft has reached terminal velocity when doing tests. In fact you only need to test the terminal velocity with the parachute deployed, then afterwards calculate how high you need to drop the craft from to achieve the same speed and further on just test by dropping it from that altitude above the parachute cutoff point.

For example if your cutoff point is 5 meters from the ground and terminal velocity is 5 m/s with the chute, then you only need to drop it from roughly 6 meters or so to simulate the cutoff speed and altitude.

Ingenious!

Also what I'm thinking is that the safest bet would be to use a analog altimeter (strings with weights attached to them) as someone already suggested. Use 4 and when the weights hit the ground, they release the switch for the landing rocket.

Sounds like a lot of weight. A remote activation sounds better: what do you think, chris?

As Duxwing calculated, you have very small margin of error to drop the egg. What I'd suggest is you use the water rocket only to touch down, have 4 landing legs with shock absorbers and a switch to sense when the full weight of the rocket is on the legs. This switch releases the egg from precalculated drop height (1-2 centimeters off the ground when landed) and simultaneously ignites solid rocket boosters that lift the craft off the ground. These are available commercially but I don't know about your contry's legislation, at least in my nanny-state they're very highly regulated and you need a license. But they are powerful and light weight.

Thanks. I'm glad I calculated correctly! We cannot use your plan because chris specified that the egg must be the first thing to touch the ground. Going Kerbal (complexity, SRBs, and complex SRBs) on this problem sounds dangerous...

In ideal situation you'd have the lander cut the chute, come down in freefall (remember aerodynamics!), weights hit the ground and ignite water rocket at exactly known altitude, craft lands (can be a bit bumpy too!), switch drops the egg and ignites the solids and the DragonEgg is laid in a puff of smoke, steam and fire while the lander soars off and possibly gets all tangled up in the still-airborne parachute and catches fire.

Hence my point about danger.

--

@chris Reading your posts, I have noticed that you often use solutions that seem so complex as to not have been made with elegance--the chief engineering virtue behind efficacy--in mind. I therefore worry that your solutions will cause more problems than they solve, causing you to become distracted by the technically-sweet complexity whilst your project remains unfinished. What do you think?

-Duxwing

Edited July 7, 2014 by Duxwing