Sunday, February 28, 2010

Preliminary Acceleration Margins for Baseline Pod

The baseline ramjet strap-on pod is illustrated in figure 1. It is a very clean cylindrical shape of length-to-diameter ratio near 8. The ramjet inlet is a translating-spike pitot type, all external compression, with a single 30o cone angle. Hidden in the air plenum are several necessary equipment items, and the wheel well for the steerable nose wheel. The pod carries its own fuel supply, and need not draw fuel from the core vehicle.

This design concept has evolved slightly from earlier concepts, mainly in terms of flight controls. The earlier wrap-around fins have been replaced by fixed fins, and dive brakes whose mechanisms are hidden in the ramjet nozzle recess. The lower pair of fins has replaceable skid tips, thus comprising the main landing gear.

Figure 1. – Baseline Ramjet Strap-On Pod Concept

The pivot wing is about 2/3 of the body length, and can support sea level stall speeds in the neighborhood of 120-140 mph. The design calls for fuel depletion and stage-off at maximum 100,000 feet Mach 6 conditions in near-vertical flight. The dive brakes are fully deployed for fastest deceleration to subsonic speeds, at which point the wing is deployed. Using the dive brakes differentially for steering forces, the pod then spirals down to a land landing, under remote control from the ground.

Estimates for component weights in this design are based upon the X-15 rocket plane, arguably the most inexpensively-reusable rocket vehicle in history. Its inert mass fraction was very close to the 40% used for this concept design. One can assume titanium structural members with Inconel-X skins and inlet duct hardware, and insulated steel fuel tankage located inside, away from the hot surfaces. Bladder fuel expulsion is assumed. This construction approach is adequate all the way up to Mach 6 without heat protection, as was shown by the X-15 program.

The ramjet combustor is ablatively-cooled with DC-93-104 silicone, and the integral boost propellant charge is case-bonded in place upon that insulation, using the bond technology developed for ASALM-PTV. The inlet port cover is frangible glass with insulation. The booster nozzle rides with an O-ring seal on the ramjet throat, held in place by finger struts slotted into the nozzle bell. These are released by an outward-opening clamp, similar to the SA-6 “Gainful” ejectable booster nozzle. A booster pressure sensor triggers clamp release, the shatter charge for the port cover, initiation of fuel flow, and a pyrophoric magnesium ignition flare.

The pod is modular, in the sense that the inlet section is separable from the fuel tank and duct section, in turn separable from the ramjet-and-booster chamber section. It is assumed that a freshly-insulated and propellant-loaded ramjet chamber is substituted for the fired unit. The fired chamber is, in turn, refurbished and reloaded, for assembly onto another vehicle later. Modular separability thus enhances access for refurbishment.

On a unit area basis (So = 1 square foot), the weight statement estimated for this design is as follows. The ejectable items are 5 lb for the booster nozzle and 2 lb for the port cover in the 13.54-inch diameter corresponding to So = 1 ft2. In the absence of better information, it is simply presumed that all of these items scale in proportion to So.

Wrjbo.......133 lb.......weight at ramjet burnout
Wf...........29 lb.......ramjet fuel weight (JP-5 density)
Wrjig.......159 lb.......weight at ramjet ignition
Wejecta.......7 weight of transition ejecta
Wbbo........166 lb.......weight at boost burnout
Wp..........184 lb.......weight of booster propellant
Wbign.......350 lb.......weight at booster ignition

Estimated booster performance is for a non-aluminized AP-HTPB propellant system that averages near 2000 psia chamber pressure. The nozzle is “perfectly expanded” at sea level, and under-expanded as it climbs. Average thrust per unit reference area is Fth/So = 5540 lb/ft2. Average Isp at sea level is 250.7 sec. The estimated exit area proportion Ae/So = 0.172, and the nozzle expansion area ratio is 15:1.

An actual trajectory estimate has not been made, in part because no core vehicle has been defined for this strap-on to assist. However, a constant-acceleration rough guide was calculated for vertical flight to Mach 6 at 100,000 feet on a standard day. The vehicle must average 5.5 gees to “hit” this endpoint condition. Ramjet takeover is presumed to be Mach 1.5, which for this rough trajectory, happens at about 7500 feet.

Ramjet engine sizing and performance mapping was done with RJ-5 (Shelldyne-H) dense synthetic fuel. However, figures should be quite similar with JP-5 (Jet-A) or RP-1, both petroleum-derived standard kerosenes. Standard kerosene density was used estimating vehicle and fuel tank dimensions. Takeover fuel flow rate per unit reference area was 1.67 lbm/sec-ft2. Peak flow flux was 1.75 lbm/sec-ft2, in the neighborhood of Mach 2.5 to 3.9, and 10,000 to 20,000 feet. Minimum flow rate flux was 0.11 lbm/sec-ft2, at the Mach 6, 100,000 feet condition. Thus fuel flow turndown ratio looks “reasonable”.

Using previous performance mapping results, plus a crude estimate of pod aerodynamic drag, the self-acceleration capability of the pod is then its thrust minus its drag (thrust margin), all divided by its weight. Net jet thrust was used, with all additive and spillage drag lumped into airframe drag. This self-acceleration figure was calculated for both the ramjet ignition and burnout weights, to “bound” the results. Calculations were made as a function of Mach number, parametric on several altitudes from 5000 to 100,000 feet.

One should note that this thrust margin-over-weight approach provides an estimate of level flight acceleration capability. For the ability to accelerate vertically, the calculated self-acceleration should exceed 1 gee. The following figures show that low altitude acceleration potential is quite good from Mach 1.5 to a little short of Mach 4. At the higher altitudes, there is at least some acceleration potential out to just over Mach 5. However, even the Mach 3 peak values of acceleration potential are inadequate for vertical acceleration at 80,000 and 100,000 feet. It is still capable of vertical acceleration at 60,000 feet to Mach 5, but not in the 5-gee range. For improved high-Mach number performance, the inlet spike may well need to be multi-angle, or even “semi-isentropic”.

Figure 2. -- Self-Acceleration Potential Near Ramjet Takeover

Figure 3. – Self-Acceleration Potential at 10,000 Feet

Figure 4. -- Self-Acceleration Potential at 20,000 Feet

Figure 5. -- Self-Acceleration Potential at 40,000 Feet

Figure 6. -- Self-Acceleration Potential at 60,000 Feet

Figure 7. -- Self-Acceleration Potential at 80,000 Feet

Figure 8. -- Self-Acceleration Potential at 100,000 Feet

Although this is neither a realistic design study nor a full trajectory calculation, four important conclusions can be drawn from these results.

First and foremost, this kind of high-impulse thrust assist actually looks very promising for launch applications of all kinds, both vertical stage rocket, and hypersonic carrier aircraft launch. In large part, the attractiveness of ramjet-assist derives from the integral booster technology employed in this study. Such booster technologies were unavailable in the 1950’s when launch technologies were first being developed, appearing for the first time in 1967 with the SA-6 “Gainful” missile system. Subsonic-combustion ramjet technology has been operational since about 1950, but was “dead weight” from launch to takeover without the availability of integral boosters. (Note also that there is no compelling reason why a liquid or hybrid integral booster could not be developed.)

Second, without a more sophisticated inlet pressure recovery design than the single-angle cone used here, attractive levels of vertical ramjet acceleration capability all the way up to Mach 6 speeds at high altitudes appears to be just barely out-of-reach. That is not to say that useful horizontal-flight capability at Mach 6 is unavailable, even with this fairly simple inlet design, for these numbers show positive thrust margins to about Mach 5.5 at 80,000 and 100,000 feet. Remember, the pod drag used here may be too high, as it corresponds to a gun projectile, and includes a lot of nose pressure drag and base drag contributions that would be missing with a flow-through nose-inlet engine. (That drag data came from Hoerner’s self-published “Fluid Dynamic Drag”, section 16 page 21, figure 30.) Ultimately, for vertical launch, Mach 5 may be a better “target” terminal speed, while Mach 6 is more feasible for horizontal flight of hypersonic carrier aircraft.

Third: thrust and drag decrease with altitude, while weights do not. There is an altitude above which the acceleration capability of the ramjet becomes unattractive, simply because the weights are too large. For the vertical launch assist, this altitude is lower, simply because higher acceleration levels are required (the carrier plane can essentially “cruise” horizontally). Given these results with these assumed numbers for drag and weights, that vertical launch limit may be nearer 70,000 feet than 100,000 feet. This can be seen in the peak thrust margins shown in the plots for 60,000, 80,000, and 100,000 feet. Remember, to accelerate at all vertically, this must exceed 1 gee, and to maintain attractive levels for this kind of launch, it should be nearer 5 gees. But, for the carrier plane scenario, all that is needed is a nonzero acceleration potential, available at 100,000 feet to Mach 5, even with the crude design concept explored here.

Fourth, the ramjet strap-on pod explored here could just as easily serve a hypersonic carrier plane as the vertical stage rocket. The only difference is flying a little higher and faster with the hypersonic carrier plane, and a little lower and slower with the vertical stage rocket. Speculatively speaking, appropriate design “targets” for pod ramjet burnout conditions might be around Mach 4.5 to 5 at 70,000 feet for vertical launch, and Mach 5.5 to 6 at 100,000 feet for carrier plane launch. These are only crude estimates, and could shift dramatically with better inlet designs and more appropriate drag and weight data.


  1. Hello, Mr Johnson, I have been working on analysing rocket trajectories concerning gravity losses. As you may know gravity losses can be reduced by increasing the thrust/weight.

    Now unfortunately it seems that one just cannot have a rocket with an intitial thrust over weight of around 5 what you are proposing. This due to the economics of high thrust engines, the requirement to perform a fast pitch over to initiate a gravity turn under high stresses and low in the atmosphere, a much higher maximum dynamic pressure, increasing acceleration when using liquid rocket stages (satellites cannot bear the vibrations encountered at say 10 g's) and maybe others.

    Also, the idea of waiting until 80,000 feet and mach 6 to start your gravity turn does not make sense since you want to build up your circular velocity as soon as possible. But where I might find an application is to use ramjet engines at boosters to increase the acceleration from say 2.5 to 4g's after the maximum dynamic pressure is reached. However this peak is usually reached at 30,000 feet and at Mach 1, mach 1.5 is probably reached at 35-40000 feet. This indicates around a 30-40 seconds burn left untill the ramjets ceiling is reached.

    So, with this in mind, I have a few questions. Can other ramjet designs be made with a higher ceiling or starting at lower speeds? How much thrust can a ramjet deliver? To avoid clustering of jets, can a ramjet get near the 0.5-1 MN of thrust without getting too big (meaning +2 meters diameter and + 10 tonnes in mass?) How much fuel does a ramjet use per Newtonsecond or poundhour or whatever you use? And finally, what is your take on it? It would be nice to hear another view on my assumptions why high acceleration can't be done but please even if you disagree, also approach the question as if I'm right. Thank you very much.

  2. Edit: Based on more precise data: would it still be a viable concept if ramjet takeover occurs at 27000 feet and burnout happens at 90000 feet at mach 5? Could one perhaps design the ramjet for takeover to occur at for example Mach 1.2 at 21000 feet? I do not see the advantage of having the ramjets attached after the self acceleration potential goes under 1, thus it would be essential to at least attain a self acceleration potential in excess of 1 during the entire burn. In fact using the ramjets as boosters, the self acceleration potential should be greater then the acceleration of the launcher which could be assumed to be about 4. Based on your graphs, this would only be the case for maybe a 15 second window, probably rendering my low acceleration concept inefficient.

  3. This one is for FatJohn 9-13 and 9-14: I'm not so sure about going much lower in takeover Mach with the supersonic-designed ramjet inlet I used in my study. For one thing, the external shock detaches from the spike below Mach 4, drastically reducing air capture.

    As for rocket accelerations, we used 10 to 20 gees quite routinely in solid propellant missile work.


  4. For Fatjohn 9-13 and 9-14: Sorry, I forgot how to tell you how to get fuel flow numbers. In the data I posted for any particular Mach-altitude point, there are both thrust (lb on a 1 sq.ft area engine, or really lb/sq.ft frontal thrust density for any size engine) and Isp (sec, which is really lb-sec/lbm) data. Divide thrust by Isp to get fuel flow rate in lbm/sec for the 1 sq.ft engine, or really lbm/sec-sq.ft for any size engine. The reference area is the outside of the biggest cross section, at the combustor.