I incorporated a Kalman filter into the altitude control loop; it estimates altitude and velocity from a model of the helicopter and the altitude measurement from the LIDAR Lite. It doesn’t compensate for tilt errors, so it only works for small pitch and roll angles. The dynamics model includes a lag between issuing the thrust command and when the rotor thrust reaches steady state, so a transfer function Tactual/Tcommand = 1/(tau*s + 1) goes between the controller transfer function and the plant. This plot shows a climb to 20 m then a descent at 1 m/s. The black curve is the Kalman filter altitude estimate and the red points are the noisy LIDAR measurements.
This plot shows the commanded control output and the actual control output for tau = 0.9 seconds.
I tested the LRD-3 Aluminum air tank and it burst at 828 psi (57.1 bar).
Dry Mass: 2.34 kg (5.16 lbm)
OD: 7.271″ (18.47 cm)
Wall thickness: 0.097″ (2.46 mm)
Ultimate strength: 30,204 psi (208.2 MPa)
This ultimate strength is about 10% higher than what I computed for the 5 gallon tank, but still well below the 42 ksi UTS I’ve seen published for 5086-H116. I posted the entirety of the burst test video (burst occurs 2:09) so you can see the tank balloon as it is pressurized. The catalog diameter of the tank is 7″, but I measured a 7.271″ OD after the test; I neglected to measure the tank OD before the test. In retrospect, it worked in my favor that the UTS was lower than expected because my tester and pressure transducer are only good to 1000 psi.
For the vehicle, I’m considering downsizing from 5 gallon propellant tanks to 3 gallon tanks and from 250 lbf thrust to 180 lbf. Low Rider Depot makes a 3 gallon version of the 5 gallon tanks I’ve had success with and I purchased one for burst testing. Assuming engine thrust = 180 lbf, Isp = 140 seconds, O/F = 1.1, and runtime is 20 seconds, I’ll need 1.865 gallons of ethanol and 1.414 gallons of LOX. I’ll need high pressure tanks to hold the pressurant and equations from Sutton Chapter 6 and H&H Chapter 5 yield similar answers for the required volume: 0.79 to 0.92 gallons of nitrogen at 2000 psi per propellant tank (pressurantSupply). Based on the dimensions I could find (OD = 4.3 inches, height = 16.5 inches), the volume of a D size medical oxygen cylinder is ~1 gallon, so I’ll need 1 of those cylinders per propellant tank. Here’s a crude version of the vehicle with the 3 gallon propellant tanks and the D size medical oxygen cylinders. The vehicle is roughly 50 inches (129 cm) tall.
I purchased two more 5 gallon aluminum tanks from KMW Performance and proof tested them to 400 psi (27.6 bar). I’m presently looking for somebody to clean one for LOX service; the local welding supply stores could not recommend a vendor for cleaning parts for LOX service. These tanks are going on a test stand, but I plan to use the same ones on my vehicle.
I also started machining the 100 lbf heatsink engine. I decided drilling the chamber and converging portion of the nozzle would be easier than working it with a boring bar, though the surface finish on the chamber ID is a little rough. I bought a 2 1/8” drill bit from eBay, a local machine shop sharpened it for $35, and the sharpened bit made quick work of drilling the chamber. Huzel/Huang say the convergent half angle ranges from 20 degrees to 45 degrees – my drill bit gave me a 60 degree half angle. The next step is to step drill a conical diverging section (15 degree half angle) and clean up the profile with a boring bar. Richard Nakka’s website has a handy calculator for forming nozzles.
Drilling the chamber and converging section. Stock is 4″ OD 1018 carbon steel.
Looking into the chamber and through the throat.
I bought this tiny trailer from Harbor Freight and I’m going to turn it into a portable test stand. Every Harbor Freight purchase is hit or miss: the 3/16″ steel plate I bought for the top cost more than the trailer kit and the wheel bearings get disconcertingly hot after short trips.
This week, I burst this 5 gallon aluminum air tank. I like this tank because it comes with five NPT ports and two brackets welded to it.
It failed at 46.5 bar (674 psi) in the heat affected zone of the longitudinal weld, basically the same location as the aluminum Harbor Freight tank.
I bought a 1000 psi (69 bar) pressure transducer on eBay for $35. I recorded the pressure with an Arduino Uno and SD card shield.
Dry mass = 3.2 kg (7.0 lbs).
OD = 8.196” (20.819 cm)
t = 0.098” (2.489 mm)
UTS = 27,512 psi (189.69 MPa)
According to the manufacturer, the tank material is 5086 – H116. From what I’ve read, the strength of the welded material is no less than the –O condition, but my UTS is less than all of the published 5086 UTS I’ve seen. I think the difference can be attributed to local thinning at the burst location.
I want to mount the tank using the brackets that come welded to it. I ran a quick analysis to see if one bracket is strong enough to hold a tank full of LOX (they appear sturdy). The weight of the tank and 5 gallons of LOX is 243 N (54.7 lbf). Based on the UTS I calculated from the burst test, I have a factor of safety of 22.9 at the bracket/tank weld.
I bought this hydrostatic pressure tester from Amazon and used it to burst a 7 gallon (26.5 L) aluminum air tank I bought on sale from Harbor Freight. I thought the aluminum air tank might make a good LOX and fuel tank.
I selected this hydrostatic tester because of the price and it has its own reservoir (I don’t always have access to a hose spigot). My only complaint is that it came with a flimsy and suspect pressure gage; I replaced the stock gage with a nice, liquid-filled one and I haven’t had any other issues. I used flexible aluminum tubing to connect the tester and vessel because it is rated to high pressure, it can be coiled for storage, and is *much* cheaper than hydraulic hose.
The tank burst at 580 psi (40 bar) in the HAZ of the longitudinal weld. I was careful about getting all of the air out of the line and tank; the actual “burst” was rather anticlimactic. The tank diameter is 10.05” (25.53 cm) and the thickness is 0.095” (2.42 mm); this gives an ultimate strength of 30,679 psi (211.5 MPa).
Amazon has a few 3, 5, and 7 gallon aluminum air tanks with NPT ports welded to them and the vendor advertises a 600 psi burst pressure.
The hydrostatic pressure tester is also handy for calibrating pressure transducers. Here it is calibrating a 250 psi transducer I bought on eBay:
I designed a 100 lbf (445 N) LOX/ethanol engine, similar to Robert Watzlavick’s heat sink kerolox engine.
The analysis is nothing more than the 1D isentropic compressible flow equations and thermodynamic data from RPA: 100 lbf engine
Propellants: 70%ethanol and liquid oxygen
Thrust: 445 N (100 lbf)
Mixture Ratio (O/F): 1.1
Specific Impulse: 221 s
Chamber Pressure: 1.379 MPa (200 psi)
Exit Diameter: 3.03 cm (1.192 inches)
Throat Diameter: 1.76 cm (0.691 inches)
L*: 119 cm (46.9 inches)
Oxidizer Orifice Diameter: 0.762 mm (0.030 inches)
Fuel Orifice Diameter: 0.787 mm (0.031 inches)
I used the free version of Rocket Propulsion Analysis to get the thermodynamic properties of the LOX/ethanol combustion products (temperature, specific heat ratio, and density) as functions of mixture ratio, chamber pressure, and alcohol concentration. RPA has a very intuitive user interface and the free version is surprisingly versatile and powerful. Version 2 includes film and regenerative cooling analysis. The student version is $200, but there’s a 15 day free trial.