|Ramjets from Jane's
Ramjets can have thrust to weight (T/W) ratios greater than 30 and Thrust to Frontal Area (T/FA) greater than 90 lbf/square inch. In comparison, a piston airplane engine has a thrust to weight ratios on the order of T/W=3 and a thrust to frontal area of T/FA=1.
As a rule of thumb for supersonic ramets, thrusts of 20-30 lbf/square inch combustion chamber cross sectional area are achieved. Normally, one estimates the inlet area as 50% the combustion chamber. 20 lbf thrust is representative of a vehicle at Mach 2 and sea level. 45 lbf thrust is representative of Mach 3.5 and 35,000 ft.
Based on these rule of thumb estimates, a ramjet sized to fit into a
6 in launch tube might produce 565-1,273 lbf of thrust and a 12 inch ramjet
might produce 2,260-5,090 lbf of thrust. A 10 ft diameter tube would allow
a ramjet which produces 226,000-509,000 lbf of thrust and a 15 ft diameter
tube would allow a ramjet that produces 510,000-1,147,000 lbf of thrust.
Based on calculations from "Jet Propulsion," 1955, pgs 22-23, ramjets have the following performance potentials. Actual performance will be a bit less. These Isp's are based on kerosene fuel, hydrogen will give roughly twice the Isp.
Mach No T/FA T/W Isp P/Po 0 0 0 0 0 0.5 7 200 1.0 11 750 2 1.5 17 14 1,300 4 2.0 35 20 2,000 7 2.5 76 26 2,400 15 3.0 97 30 2,400 28 3.5 94 30 2,000 50 4.0 83 26 1,600 4.5 1,550 5.0 1,500 6.0 1,300 7.0 1,100 T/FA - Thrust (lbf) per Unit Frontal Area (square inch) T/W - Thrust (lbf) per Unit Weight (lbm) Isp - Fuel Specific Impulse (Stoichiometric) Above Mach 4 the source is Zipkin and Nucci P/Po - Compression Ratio (source not recorded)
RAMJET ENGINE NOTES"Calculations based on equilibrium expansion in the exit nozzle show that the conventional subsonic combustion engine should achieve over-all efficiencies of 40-50% in the Mach 5-8 speed range and should be capable of producing useful thrust to at least Mach 10." (Dugger, Gordon L., "Comparison of Hypersonic Ramjet Engines with Subsonic and Supersonic Combustion," Combustion and Propulsion, fourth AGARD Colloquiem, Milan, April 4-8, 1960, pg 84)
Jet Engine Afterburner Flameholder/1Jet Engine Afterburner Flameholder/2
These images show the afterburner flameholder on a modern jet engine.
This image shows the T-38 swirl type afterburner flameholder. This engine
was cut open and painted for public display.
For some ramjet builders the idea of cutting and welding thin sheet metal may not be appealing. One thought came up while talking with engineers was to carve nozzles out of other materials. One material that should work is pumice, a porous volcanic rock. This material is light weight, easily worked, and can withstand very high temperatures. Besides rock shops, it can often be purchased at restaurant supply houses in block form (it's used to clean grills). If a smoother surface is desired you can purchase a ceramic paste from insustrial supply houses, such as McMasters-Carr. Another material that might work is a hardwood such as oak. Oak has been used for rocket nose cones for decades. As it heats it chars to fibrous carbon. As a ramjet nozzle it will ablate and the throat will enlarge, possibly improving performance. The amateur rocket community has a number of materials they use, one being chimney firebrick mortar.
Muffler shops have tools that will expand and compress mild steel pipe for auto exhaust systems. The metal may be good enough for the nozzle making production quantities inexpensive.
One way to atomize the fuel is to mix it with high pressure air before
injection into the combustion chamber. For small ramjets, the ram air can
be ducted through a small jet pump to both mix it and pressurize the injectors.
Using the acceleration formula the ramjet would have to have maintain roughly 3.5 g to go from 2,000 fps at sea level to 5,000 fps at 100,000 ft. The flight time for this was 29 seconds. Using a spreadsheet and considering Q (pressure and velocity) it looked more like 4 g would be required initially because of lower thrust capability above 80,000 ft.
Plugging the velocities and altitudes from the spreadsheet into a ramjet model of a 4 in. diameter tube/ramjet and 3 in. rocket gave the following results. Drag was calculated separately.
Mach Altitude Thrust Drag Excess Thrust No ft lbf lbf lbf 2.0 0 215 58 157 2.5 10,000 367 62 305 3.0 22,000 534 55 479 3.5 35,000 608 42 566 4.0 50,000 540 26 514 4.5 75,000 237 10 227 5.0 100,000 ? ?Chamber pressures were as high as 250 psi. Temperatures were not calculated but would probably peak at about 3,000 F.
Drag is calculated as:
D = 1/2 rho.v.v.Cd.l rho = density (sea level = 0.002378 slugs) v = velocity in fps Cd = coefficient of drag (see aero books) l = characteristic length (frontal area for missiles) in square feet ex: 3 in. diameter missile at Mach 2.5 and 10,000 ft. Atmospheric density ratio (Mark's) for 10,000 ft = 0.7385 Frontal area for 3 in. diameter = 7.07 in.in = 7.07/144 sq ft D = (0.5)(0.002378)(0.7385)(2,500)(2,500)(0.23)(7.07/144) = 62 lbf===========================================
The graph below shows a rough approximation of how ramjet Isp varies with fuel/air mixture. Not included are corrections for drag at zero fuel flow, generally higher Isp in the lean region, and slightly higher thrust in the rich region due to higher mass flow. These are not expected to change the curve dramatically.
Theory says that the Isp will reach about 2,400 seconds at a stoichiometric fuel/air ratio (about 1/17). Under real conditions the Isp will usually be somewhat less, typically between 1,200 and 1,700.
It has been recommended that the amateur ramjet be operated on the lean
side because a. it will reduce the combustion chamber temperature making
materials selection simpler, b. it will increase Isp (the figure needs
correction), and c. it offers smoother throttling.
Note of 18 Aug 99. This picture is incorrect and will be redone. The highest Isp occurs at a fuel/air ratio of about 1/60, very lean. It has a very steep rise from drag (zero fuel) to peak Isp, then a shallow drop to stoichiometric, then a steep dive when run fuel rich. The highest thrust occurs at stoichiometric.
The graph below shows a rough approximation of ramjet thrust with increasing fuel flow.
Thrust reaches it's nominal rating at a stoichiometric ratio. Operating
lean reduces thrust but allows a fairly responsive thrust control.
Note of 18 Aug 99. This graph is also incorrect. Thrust actually falls above stoichiometric, at least at normal speeds, due to the excess fuel cooling the exhaust. Above Mach 7 the high temperature causes dissociation of the exhaust molecules, especially the CO2. The O2 is then combusted with the excess H2 causing a hotter flame temperature and higher thrust.
Combining these two curves provides good incentive to operate in the
lean region for cooler temperatures, good Isp, and good throttleability.
The data below is from a ramjet performance estimating program. This low range is probably outside the intended operating envelope for the softare and so should be taken with a grain of salt. However, it does agree with well with the text books.
Mach T/I Isp No. seconds 0.2 167 223 0.3 164 218 0.4 188 250 0.5 244 326 0.6 346 440 0.7 497 533 0.8 678 625 0.9 889 715 1.0 1110 810 * 1.1 1408 888 1.2 1740 965 * 1.3 2103 1029 * Interpolated to complete the chart below.
This Page Last Updated 18 Aug 99
Ramjets (not to be confused with scramjets) could easily operate in the Mach 7-9 region and possibly above Mach 12. Shorter tubes and/or lower pressures could be used if the ramjets were operated less efficiently. In transitioning from subsonic to supersonic there is a strong drag rise around Mach 1.0. This drops off quickly and reaches a minimum at about Mach 1.2. This would be a good alternative to begin ramjet operation but could complicate the ramjet design and/or limit the maximum velocity. For amateur rocketeers this could be a good tradeoff against the expense of a longer tube and higher gas volume. A subsonic ramjet could be used if lower costs were needed.
Two or more ramjet stages could be used in tandem, each optimized for velocity ranges such as Mach 2 to 7 and Mach 7 to 12. This could be especially advantageous if different fuels (such as kerosene and hydrogen) were used for each ramjet stage.