Gas Powered Mortar Launch Of A BFR Rocket

Much of the fuel and oxidizer of any rocket that is launching a satellite is burned just getting up to about one thousand miles an hour.  The first part of the launch is particularly inefficient compared to a gun. You can think of the fact that rocket thrust depends upon the momentum change of the expelled gas, while the relative kinetic energy contained in the gas versus the rocket changes as the speed increases. When the velocity of the rocket equals the velocity of the gas expelled from the rocket engine, the thrust and therefore most of the chemical energy of the propellant is going to  either raise the rocket against gravity or to increase the kinetic energy of the rocket (in a vacuum), whereas when the rocket is sitting still nearly all the kinetic energy due to the gas velocity is carried away with the exhaust gas, in a sense.

I propose a Jules Verne style big cannon, or more descriptively a mortar to launch a rocket. The pressures involved are much lower than the pressures in a military cannon, or even an ordinary mortar. I envision pressures typically around 20 bar behind the rocket. 

Consider as an example of a large rocket to be launched by the proposed large gas mortar the SpaceX rocket called the BFR. This rocket is 9 meters diameter for  most of its length, but has fins on its upper stage that bring out the total diameter to about 14 m. I know from a talk by Elon Musk, the October 2017 SpaceX update concerning plans for the 2022 Mars mission, that the BFR upper stage is designed to carry 1200 tons of fuel plus oxidizer, with an estimated 85 tons dry weight. The cited mass for the fully loaded BFR is 4400 tons, which means that the booster stage would weigh 3115 tons. If the same ratio between wet weight and dry weight exists for the first stage rocket as for the upper stage, then the lower stage would be carrying about 2865 tons of fuel and oxidizer.  Musk said in his talk that the initial thrust is to be 5400 tons, delivered by 31 Raptor rocket engines, which if we take gravitational acceleration on Earth to be 9.81 m per second squared, means the thrust would be 53,000 kilonewtons. This implies that the initial acceleration of the rocket is 1.227  times normal Earth gravity; therefore initial vertical acceleration of the rocket is only about  2.23 m per second squared because the accelerating thrust of 9810 kilonewtons represents only about (.227/1.227)% of the total thrust, most of which is going to simply counter gravity at the beginning of the launch.  Consider how much more gravitational work would be done at the beginning of rocket firing if the overall rocket has a high vertical velocity when the rocket is ignited.

An optimum vertical rate of ascent of the BFR rocket at the time of rocket ignition following a mortar launch exists such that the rocket is neither accelerating or decelerating when it leaves the launch tube, right after rocket ignition. In other words the vertical velocity should ideally be such that the aerodynamic resistance is equal to the thrust supplied by the rocket over and above that which is needed to balance the gravitational force due to the mass of the rocket. That is an aerodynamic calculation, to which I do not have the answer right now. However it is obvious from the high net thrust of 9810 kilonewtons that this represents a great speed, probably supersonic, and as the rocket rises the decreasing air drag and the reduced mass of the rocket would allow the rocket to accelerate further. If the initial rocket velocity from the launch tube is supersonic, then the vibration that occurs as the rocket passes the speed of sound would not occur, which simplifies the structural design of the rocket. 

In considering the efficiency of a rocket, it is useful to look at both forms of work being done as the rocket is lofted into space: first there is an increase in gravitational potential energy as the rocket is lifted, and second there is the increasing kinetic energy of the rocket. By  accelerating the rocket in a mortar launch prior to igniting the rocket, then simply holding the speed constant just after the time the rocket ignites upon its vertical exit from the launch tube, the rate of doing gravitational work in lifting the rocket becomes much higher. To be specific, when the rocket launches from a standing start the gravitational work in the first second would be 4.4 million kilograms X 1.115 m X the acceleration of gravity, which is 43.75 megajoules. In comparison, the gravitational work in the first second of rocket firing, given a launch velocity of 1000 m per second would be 4.4 million kg  X 1000 meters X the acceleration of gravity on Earth (9.81 m/s), which is 39240 megajoules. This means that 804 times as much gravitational work is accomplished by the rocket in the first second if the initial velocity is 1000 meters per second. The increase of kinetic energy in the first second for the BFR accelerating from a standing start is 1/2 X 4.4 million kg X 1 second X 2.23 m/s2 upwards acceleration, which is 11.3 megajoules. By comparison, given an initial velocity of 1000 m/s for the BFR rocket, the kinetic energy increase over the first second would be  9823 megajoules, which is 869 times higher than the increase of kinetic energy during the first second of firing for the rocket from a standing start.  Here I neglected air drag for sake of simplicity, and assumed that the rocket velocity becomes 1002.23 m/s during the first second of firing given an initial velocity of 1000 m/s, although the optimum method to operate such a mortar launched rocket may well be to maintain a constant velocity at first due to the high aerodynamic drag in the troposphere, in which case there would be no acceleration during the first second.

At any time one can describe the total work being done by the rocket motor as a sum of the acceleration work and the lifting work. As the velocity of the rocket increases, and as the direction of motion of the rocket approaches horizontal, an increasing portion of the work is going towards the acceleration of the rocket, but in the first stage a lot of the work is the lifting of the rocket against gravity.

The gravitational work component scales with initial velocity, and so is quite low at the beginning of flight of the rocket for a launch from a standing start. If however the rocket is given a high initial vertical velocity at the time that the rocket begins firing, then the rate of working against gravity is very high. Similarly, because the rate of increasing kinetic energy scales with the square of velocity, the rate of kinetic work is also dramatically increased by giving the rocket an initial velocity. That means that the energetic efficiency of the rocket is greatly increased by means of accelerating the rocket prior to firing it.

In order to fit the SpaceX BFR rocket into a launch tube, the tube needs to be wide enough to accommodate the fins on the upper stage. That implies an approximate diameter for the launch tube of about 14 m. In addition, the rocket must sit on a sabot that forms a gas tight seal below the rocket and which is able to support the mass of the rocket while it is being accelerated. I estimate that this sabot would weigh 200 tons, which implies a total launch weight of 4600 tons.  Given this and the other assumptions outlined above, I calculate that 113 million newtons would be needed to cause an upward acceleration of 4G (G = 9.81 m/s) for the BFR rocket in a mortar launch.  That implies that a passenger on board the rocket would experience an effective gravity of 5 times normal gravity on Earth at the beginning of the launch. This implies a pressure difference of 1.05 megapascals, about 160 pounds per square inch, between the pressure behind the rocket and in front of the rocket.

In one possible scenario, at the very beginning of the launch, non-combusting gas pressure alone would begin the acceleration. Thereafter combustion would begin within the gas phase behind the rocket. Acceleration would vary at different times after the rocket first begins to move. I believe an average acceleration corresponding to 3G, 29.43 m/s2 is achievable. 

As an example, consider a barrel length in front of the rocket L = 5 km with an effective average acceleration a = 29.43 m/s2.  We can solve for the time of flight in the barrel as the square root of the quantity 2L/a; the answer is that the rocket is in the barrel for 18.43 seconds. This corresponds to an exit velocity of 542 m/s. This is way less than orbital velocity, but it is comfortably supersonic, and would greatly increase the initial efficiency of the rocket and substantially increase the cargo mass that could be delivered to orbit by the rocket.  By using higher accelerations and longer launch tunnels it is possible to get much higher speeds, potentially approaching orbital velocity, though that would require a very strong rocket capable of withstanding both the accelerations and the aerodynamic forces of hypersonic travel through the lower atmosphere. 

Because the air drag will be very high in the lower atmosphere, it may not be desirable to accelerate substantially after such a proposed mortar launch until one is above the troposphere.  This might require that the rocket engines would be throttled down to avoid excessive aerodynamic stresses and energy loss. For the mortar launch in particular, Max Q would probably occur at the muzzle of the mortar launcher as the rocket enters the atmosphere at high speed.

I think the optimum way to throttle the rockets between the time of a mortar launch and the achieving of extremely low atmospheric pressure is to maintain a nearly constant speed while traveling through the lower atmosphere. The high throttle ability for the Raptor rocket combined with a high velocity mortar launch would enable something unique in rocketry, a sustained period of Max Q. The reason this is could be important is that it enables a complete use of the rocket’s full capabilities to the maximum effect. Rocket thrust and acceleration could be modulated to keep the aerodynamic drag close to Max Q, perhaps well up into the stratosphere.  Max Q may be what limits the maximum muzzle velocity, but muzzle velocity may also be limited by the length of the tunnel, the maximum acceleration, and the structural capabilities of the rocket itself to withstand acceleration. In any case, a supersonic mortar launch would surely require a specially-designed rocket.

Somewhere between 25,000 to 40,000 meters of elevation, the atmospheric pressure will be low enough for more efficient, higher expansion ratio rockets to be used, such as the Raptor rocket that has been developed by SpaceX for the second stage of the Falcon 9 rocket and the BFR. I do not  think it would be practical to use the mortar launch alone to get the rocket high enough so that the more efficient high-expansion-ratio Raptor vacuum rockets could be used for the rest of the trip, especially since this implies allowing a vast deceleration prior to turning on the high expansion rockets, which reduces efficiency as described above.

Perhaps the high expansion ratio rockets may be used in the lower troposphere provided that the rocket is traveling fast enough to create a vacuum behind the rocket.  I do not know what speed would be required to make the vacuum type Raptor rockets work in the troposphere; I intuit that a minimum speed well above the speed of sound in air would be necessary, possibly corresponding to the exit velocity of the gas coming out of the rocket, which is around 3200 m/s.  I do not believe that such a hypersonic launch would be practical in any case for a rocket carrying humans.

I visualize a combination of a gas gun with no combustion and a gas gun in which combustion occurs. In particular, I envision a launch tube that is 5.5 km long, and has been dug by a tunnel boring machine.  The projectile is a BFR rocket and the diameter of the tunnel is 14 m, in which some of the annular clearance between the rocket and the tube launcher will be occupied by sliding bushings that may also provide some lateral reinforcement of the rocket against buckling. The sabot would support the rocket and also have the function of forming a gas tight seal between the rocket and the launch tube. The rocket projectile is located 5 km from the exit end of the launch tube, with half a kilometer of compressed combustible gas behind the rocket. It is highly desirable that the 5 km of the launch tube in front of the rocket be evacuated. Some means of vacuum sealing at the exit end of the launch tube would be provided such that the end seal is intact until the rocket punches through. This basic setup is used as the basis for a series of examples below for various launch scenarios.

Examples of the Invention

Let's consider a very high velocity launch.  This could not apply to any current rocket, because present-day rockets are not designed to allow the very high accelerations that are considered here, for example an average acceleration of 1000 m/s2. Though this would be a very high acceleration for a rocket, it would be low for a gun. For maximum velocity, the mass of the rocket would have to be much less than the mass of the fully-loaded BFR rocket, for example 500 tons or less.  The bottom 0.5 km behind the rocket prior to launch would be filled primarily with hydrogen gas, possibly a mixture of hydrogen and oxygen. The pressure in the gas chamber would be raised up to a level which is able to accelerate the rocket at the maximum allowed acceleration strictly by gas pressure, prior to combustion of the gas mixture. I suggest this could be as high as 100G, about 1000 m/s2. If one builds a system capable of 1000 m/s2, one need not use that capability for every launch. In particular it might be practical to operate the gas launcher at 100G for robotic cargo ships, while you also launch space tourists at maximum acceleration of 3G, for example.

In the case of a high acceleration hypersonic launch, it is particularly desirable that the compressed gas chamber behind the rocket prior to launch should be filled with primarily hydrogen gas, perhaps containing oxygen at a sub-stoichiometric ratio, so that the post combustion gas is still predominantly hydrogen. Several variants on this theme are possible, for example, one could fill the entire 0.5 km compressed-gas region behind the rocket prior to launch with hydrogen at the beginning, then introduce a stoichiometric mixture of methane and oxygen from the bottom; this guarantees that the gas right behind the rocket is nearly pure hydrogen while still enabling a combustion driven pressurization from behind, after the initial part of the launch which would be accomplished strictly by the stored PV energy in the compressed gas. At the very beginning of launch some form of restraint would be released that would enable the high pressure hydrogen gas to begin pushing the rocket up the launch tube. As the hydrogen expands, the acceleration will decrease until the time where the combustible gas mixture below the hydrogen zone is ignited.  At that time acceleration will increase again.

I envision another hypersonic launch scenario in which oxygen is blown into the launch tube from jets on the sides of the launch tube, only after the rocket is fully loaded and ready to go, or perhaps even after the rocket begins to move. In the very beginning all the gas behind the rocket could be hydrogen but as the hydrogen expands there could be oxygen injected into the hydrogen at points behind the moving rocket. The injection of the oxygen increases the pressure, leading to a greater acceleration of the rocket even before a subsequent ignition of the hydrogen oxygen mixture. It is also possible to inject oxygen in such a way as to create a pocket of an explosive hydrogen and oxygen mixture at the back end of the launch tube, with the portion of the launch tube just behind the rocket comprising mainly hydrogen. This hydrogen and oxygen mixture would be ignited after the rocket has been moving for a second or so. 

The importance of the hydrogen content of the propellant gas is that the speed of sound scales with the inverse of the square root of molecular weight at any given temperature. For example, the ratio of the speed of sound in hydrogen compared to the speed of sound in oxygen is related to the molecular weight of oxygen, MWO2 and the molecular weight of hydrogen, MWH2 by this formula:


As a result the speed of sound in hydrogen is around 4 times faster in hydrogen compared to oxygen. The speed of sound in the propellant gas limits the maximum muzzle velocity from a gas powered gun. I think it is therefore desirable for a maximum velocity launch to have the gas immediately behind the rocket be nearly pure hydrogen. I think it will be possible to nearly achieve that by using a long launch tube with a combustible gas mixture only in the end of the tube farthest away from the rocket. Note that the combustion velocity in hydrogen oxygen mixtures can be above 2000 m/s, depending on temperature and pressure.

A desirable high velocity launch scenario involves a hydrogen oxygen mixture with more than stoichiometric amounts of hydrogen. One can visualize a hybrid launch system in which a high-hydrogen gas mixture with oxygen content close to the minimum concentration of oxygen to make the gas mixture combustible initially fills the part of the launch tube behind the rocket. In this scenario, the combustible gas mixture initially accelerates the rocket like an ordinary air gun, but then the hydrogen-oxygen mixture is ignited sometime after the rocket begins its forward motion in the launch tube, after the acceleration is reduced from its initial maximum to some selected level. The ignition would occur at the opposite end of the launch tube from the now rapidly moving rocket,  perhaps a few seconds after the rocket is released, or perhaps the combustion wave begins the acceleration. After ignition, a combustion wave will travel up the column of combustible gas causing compression of the gas in front of the wave, leading to an increase of acceleration. Even after the combustion wave reaches the rocket, one could still use additional oxygen injection from the sides into the hot steam and hydrogen mixture created by the initial burn of the hydrogen-rich hydrogen and oxygen mixture for an additional boost. This form of launch is intrinsically more risky than one in which a non-explosive mixture of gases is behind the rocket prior to launch, since a premature explosion could cause greater acceleration than would be planned for or tolerable.

A hybrid concept would have the rocket loaded and ready for firing based on a non-combustible pure hydrogen gas pressure behind the rocket but then perhaps only minutes before launch the requisite amount of oxygen would be blown in. It would take only seconds or at most a minute for the gas to mix and be ready for the burning of the gas mixture. If there is excess hydrogen in the mix then the oxygen doesn't have to be thoroughly distributed to get the entire benefit of the burn of the gas. I like this scenario better than premixing the fuel and oxidizer as the lower chamber is pressurized for reasons of safety.

Consider the case of a launching mortar in which the gas below the rocket is comprised of primarily hydrogen gas at a pressure just high enough to balance the weight of the rocket with the pressure on the lower side of the sabot. The hydrogen gas contains an amount of oxygen that will react with only part of the hydrogen, perhaps between 5 to 20 mole % of all the hydrogen present.  Since the atmosphere is about 20% oxygen, a reaction of one mole of oxygen with 10 moles of hydrogen would be very similar to a stoichiometric reaction of hydrogen with air. 

Hydrogen and oxygen mixtures have higher combustion velocity than any other gas mixture I have examined. They also exhibit very high pressure ratios between the pre-combustion gas and the pressure following combustion, in spite of the fact that there are fewer moles of water formed than the moles of reactive gas. For stoichiometric hydrogen oxygen mixtures, a pressure ratio of about 70 is observed. I don't have the data for the pressure ratio from burning of non stoichiometric hydrogen oxygen mixtures but this will depend upon the adiabatic flame temperature compared to the initial temperature. I assume that the pressure ratio that occurs in a 10 to 1 hydrogen:oxygen mixture would be about equivalent to that pertaining to hydrogen air mixtures, somewhere around 5.

Consider the example of a launch initiated by a mixture of 10 moles of hydrogen with 1 mol of oxygen.  The initial pressure is .344 megapascals, or 3.4 atmospheres. This is just enough to support the weight of a fully loaded BFR rocket on a 14 M diameter sabot. The launch would be initiated by sparks or a single spark at the bottom of the hydrogen oxygen mixture, and the combustion wavefront would move with a speed close to 1000 meters per second towards the lower surface of the sabot. Even before this combustion wave reaches the surface of the sabot, the hydrogen oxygen mixture next to the sabot will be compressed by the combustion wave below.  About half a second after ignition, the combustion wave would reach the surface of the sabot and the pressure would be about 5X higher than the initial pressure per my estimate.  this would initiate acceleration of the rocket at four times the acceleration of normal Earth gravity upwards. After the initial combustion is complete, additional oxygen could be injected from the sides of the launch tube to maintain near constant acceleration. This is a complex situation which I think can be manipulated so that the oxygen injection following combustion wave propagation can be optimized to keep the acceleration of the projectile, the rocket, near constant. A potential advantage of this type of launch is that the gas remaining in the launch tube after launch would be primarily steam and could be condensed readily; this should make it easier and faster to reestablish a vacuum.

One can also envision a totally combustion driven launch, similar to that envisioned above with hydrogen oxygen mixtures, but fueled by methane air oxygen mixtures. The pressure ratio for combustion of methane air mixtures is also on the order of 5X increase in pressure, but to keep the option of a subsequent pressure boost through the insertion of additional gas, one would need to add at least some oxygen to the air methane mixture. On the other hand, the much lower velocity of the flame front in methane air mixtures allows a possibly desirable degree of control that would not be possible for hydrogen oxygen mixtures, since ignition from the sides of the launch tube can control the movement of the combustion front. Thus a region composed of compressed methane and air could exist behind the rocket initially, with a pressure high enough to lift the rocket at the target acceleration prior to igniting the mixture. Igniting combustion at the far end of the column of methane and air would compress the gas below the rocket and increase the acceleration. The low combustion wave velocity in methane and air would make it possible to control the advance of the combustion front, and potentially to even out the acceleration during the 5 km motion of the rocket down the launch tube, without resorting to controlled introduction of gases during the launch. 

A low-cost launch scenario would start with compressed air behind the rocket. If compressed air alone is used to accelerate the rocket, then the maximum velocity will be less than the speed of sound in air. For a purely compressed air based launch, the volume of air behind the rocket should be quite large compared to the volume in the barrel in front of the rocket in order to maintain consistent acceleration during the trip down the launch tube. If combustion occurs in the driving gas, then the volume of the driving gas can be lessened. Using combustion to drive the rocket launcher also substitutes chemical energy for the electric energy that would be consumed in compressing the gas underneath the sabot for a purely compressed air or compressed gas based launch with no combustion. 

In a combustion driven launch, the temperature of the driving gas is higher  than in air, so the speed of sound is higher too; this is why bullets from rifles can reach speeds of 1000 m per second, which is well above the speed of sound at room temperature for the gases that  are produced by the burning of gunpowder. Both temperature and molecular weight of the gas limit the muzzle velocity from any gun based on gas expansion; one can increase the muzzle velocity either by increasing the temperature of the driving gas, or reducing its molecular weight.

A low cost combustion driven launch would begin by introducing compressed air underneath the sabot supporting the rocket. After the rocket is fully loaded and ready to be launched, natural gas would be injected from the sides to create a combustible mixture behind the rocket. As with other methods described above involving hydrogen, the initial acceleration of the rocket could begin with simply the stored energy in the pressurized combustible gas mixture behind the rocket. Ignition of the combustible gas mixture would in this case occur after the rocket has been released and is moving down the launch tube.  Ideally the combustion wave would reach the backside of the rocket just as the rocket exits the launch tube into the atmosphere. The velocity of the combustion wave in burning methane air mixtures is far too slow to catch up with the moving rocket; however one can manipulate the effective velocity of the combustion front by igniting the gas mixture from the sides of the launch tube.

Even the lowest cost gas mixtures and a launch tube that is only 5.5 km long could still achieve a supersonic initial velocity for the rocket and so greatly increase the load delivered to low-Earth orbit for a rocket.  This is believed to be highly practical for the scenario where hundreds of launches each year are anticipated. 

A tunnel boring machine can certainly bore a 15 m diameter vertical tunnel, since many vertical tunnels larger in diameter than this have been drilled for ICBM silos. Although the silos were not as deep as that being proposed here, I believe there is no fundamental reason preventing the construction of a TBM capable of producing a 14 meter diameter vertical tunnel. (Note that 10 m diameter horizontal rail tunnels much longer than those required for launching rockets as proposed here were drilled in Switzerland.) If the rocks are selected correctly, boring the tunnel would be a small part of the total project cost. I believe a relatively thin metal sleeve could be placed inside the rock tunnel with adequate smoothness to work as a launch tube.

Another possible way to create the launch tube would involve a floating structure in the ocean, as was proposed in Project Quicklaunch. This approach has some advantages, including the fact that a seamless inner tube would be possible. However the need for the bottom of the to to withstand great pressure exerted by the ocean is a large drawback. 

I envision the rocket being surrounded by a sleeve comprised of a slippery polymer like ultra-high molecular weight polyethylene or PTFE at the outer perimeter where it contacts the launch tube. Delrin would also be very cost-effective; basically this is poly-formaldehyde, but I think it would be unavoidable in that case that you would produce formaldehyde emissions at launch, so I think UHMW polyethylene and PTFE are the most logical candidates for the sliding surface between the sleeve, sabot, and launch tube. It is also probable that some form of thermal or plasma spray process could be used to coat the steel launch tube on the inside to reduce sliding friction and/or corrosion. It is even possible that sputtering, PVD, CVD or some other coating technology that must be applied in a vacuum could be applied to the inner surface of the of the launch tube, to minimize sliding friction and abrasion against the polymer-surfaced sabot and sleeve.

Using a sabot as a gas-tight seal has the unique potential advantage of enabling the rocket to be pulled from the front rather than pushed from the back. Since structural components are much stronger in tension than in compression due to buckling behavior, one could probably achieve greater acceleration of the rocket within the launch tube if it is pulled from near the front instead of pushed at the rear by gas pressure. It is necessary in this case to be cautious about the possibility that internal parts of the rocket could contain pressurized gas when it exits the launch tube. 

The shape of the Falcon F9 rocket with its Dragon capsule from SpaceX would be particularly well suited to the concept of pulling the rocket from the front. In this case, the sabot would be placed just behind the Dragon capsule at the front end of the rocket, which has a larger diameter than the rest of the rocket. It is feasible to use the same launch tube to launch both the BFR and F9/Dragon rockets, though the sabot would be quite different for the two different rockets.

As a polymer scientist, I have several patentable ideas about how to handle such a large sabot and its critical sliding interface so as to maintain a gas tight seal during launch.

I have been imagining a launch tube that is about 5.5 km long. The maximum pressure within the launch tube depends upon the rocket mass and the maximum acceleration planned for various rockets that would be launched. For human launches and for rocket ships with an average areal density similar to that planned for SpaceX's BFR rocket, this corresponds to a pressure differential from behind the rocket to in front of the rocket between 10 to 30 atmospheres. If the same launch tube is to also be used for unmanned cargo craft, accelerations as high as 100G would be desirable; this could correspond to pressures as high as 200 atmospheres, which would have to be created through combustion.

In order to achieve supersonic launch, it is very desirable that the portion of the launch tube in front of the rocket is evacuated. I can visualize three possible methods to keep the launch tube in front of the rocket evacuated as the rocket is accelerated by gas pressure behind it:

A dome holding back atmospheric pressure could seal the end of the launch tube and be designed so that it bonds to the front end of the rocket upon impact.  In this case the ceiling dome would effectively become part of the spaceship, fulfilling the function of a heat shield during the ascent of the rocket through the atmosphere. If it is properly designed, this shield could later be used in the construction of a space station for example.

The dome holding back atmospheric pressure could be blown out of the way using shaped charges of high explosive just before the front end of the rocket exits the launch tube.

The dome holding back atmospheric pressure could be designed in conjunction with a leading edge of the rocket so that the rocket pushes the dome aside. This necessarily entails that the dome separates into sections. The dome could consist of a fiber-reinforced elastomer film, similar to those used to seal the end of a subsea missile launch tube until the nose cone of the missile rips through the membrane. Alternatively, the dome could be made up of solid pieces which are designed to part as the rocket passes through; in this case the dome would likely have straight sections that would in cross-section form a regular geometric shape such as an octagon or a dodecahedron for example, and would match the shape of the rocket nose-cone exactly.

It is desirable to limit the speed of the rocket through the thick part of the atmosphere. This is so in part because aerodynamic resistance scales with velocity and the gas pressure. I think it is most probably best for the thrust at the time when the rocket breaks through the ceiling dome and into the atmosphere to be approximately equal to the thrust required to prevent deceleration from atmospheric drag. 

To take a specific example, if the rocket is traveling at 1000 m/s at the time it bursts through the ceiling dome of the mortar launcher, it will take about 25 to 40 seconds to reach an altitude where the atmospheric pressure is low enough to enable vacuum-type rockets to work. If the rocket is neither accelerating nor decelerating at the time just after it first enters the atmosphere and ignites its rocket engines, then if the thrust is maintained constant the acceleration will increase with altitude for two reasons. First, the aerodynamic drag would decrease with altitude. Second, the mass of the rocket would be decreasing due to consumption of rocket fuel.

Let's consider for a moment the optimum location for such a tunnel based mortar launcher. The optimum place to locate a launch tube would be at high elevation right on the equator. A slight slanting of the launch tube towards the east might be desirable since using the Earth's rotation saves quite a bit of energy, and so the most economical launches are always towards the east. This however would create asymmetrical normal forces between the two sides of the sabot, which could be problematic. The Andes mountains look interesting as a launch site except for one thing: in most cases it's very important to have an ocean to the east of the launch site or at least an area with low occupancy by humans, since there is always a chance that a rocket launch will fail in such a way that the rocket will fall down. This is far less dangerous if it falls into the ocean compared to any landmass on Earth. This is why a slight tilt eastwards would be desirable so that even if all control is lost, the rocket would still fall into the sea in an accident. 

A recent book proposes Kenya as the location for a major launch site, but that might not be true if the rock there is not suitable for the deep-tunnel launch tube aspect of this invention, and in view of political instability in that region. Here are some of the considerations:

·         The launcher should ideally be near the equator to maximize the effect of the earth’s rotation to aid achieving orbital velocity

·         The launch should point east, to make use of the rotation of the Earth

·         The launcher should be located so that the end of the barrel is well above sea level.

·         The launcher should be located in a country that is politically stable.

·         The region to the east of the launcher should be an ocean.

·         The launch site should be near a suitable port from which the rocket can be transported to the launch site. 

I believe that these considerations argue for the mountains in Costa Rica, Nicaragua, Panama, or Columbia as candidate launch sites.

There are a wide variety of potential gas mixtures to power the tunnel based launcher. At the very low end of feasible launch velocity would be a purely compressed air based launch mechanism. The next level up I believe would comprise an air plus natural gas mixture, in which the initial acceleration would be simply due to the expansion of the combustible gas mixture; next, the mixture would be ignited at the bottom and a combustion wavefront would move up the tube towards the rocket. It would be particularly desirable if the wavefront reaches the backside of the rocket approximately when the rocket exits the launch tunnel. In this scenario, one can vary the energy yield from combustion by varying the stoichiometry of the combustible mixture, from the lowest explosive stoichiometry ranging up to exact stoichiometry for full oxidation of the methane. One can also add extra oxygen to the air methane mixture to boost the yield.

The next level up would substitute oxygen methane gas mixtures for the air natural gas mixtures described in the previous paragraph.

One can also envision more exotic gas mixtures such as hydrogen and oxygen as previously mentioned above. This is particularly of interest for the case in which maximum acceleration is allowed to be much higher than that which would be tolerable to human beings. Note that complex mixtures involving methane, hydrogen, air, and oxygen might allow for the control of the velocity of combustion wave propagation, as would be desirable for an optimized mortar launch.

This invention is aimed at increasing the payload to low-earth orbit for a conventional rocket, such as the SpaceX F9/Dragon or BFR rockets. An extremely important aspect of the invention is that a tunnel boring machine would be used to create the launch tunnel. This greatly reduces the cost compared to prior proposals in which the launch tube is made of metal and is in essence a large cannon barrel.  as noted above, a tunnel that is approximately 14 m in diameter would be required to launch the BFR rocket as currently envisioned; if however the fins on the upper stage of the rocket could be eliminated, the tunnel launcher would only need to be 10 m in diameter.

Note that the pressures that are required behind the rocket in the present invention are quite low compared to the pressures that  have been used in prior art cannon launched spacecraft proposals, such as the launch cannons developed in the HARP program funded by the US Army in the early 1960s. Even though the envisioned launch speed of 300-1000 m per second is only a small fraction (about one-sixth at best) of orbital velocity, the payload delivered to orbit would be greatly increased because of the very low efficiency of rockets for the low velocity portion of the flight.

In order to achieve a launch velocity of 1000 meters per second, constrained by the requirement that the average vertical acceleration is only 3G, one would need a 15 km launch tube. If higher acceleration can be tolerated, the launch tube can be shorter. I believe that accelerations as high as 10 times normal gravity on Earth would be safe for healthy people if only applied for short times, less than 20 seconds for example.  Even if a person passed out during the acceleration, this would not kill him or her. 

I envision an initial project in which the launch tube is 5.5 km long, with half a kilometer of combustible gas behind the rocket. The pocket of  compressed and/or combustible gas behind the rocket can be in a chamber that extends out to a larger diameter than the diameter of the launch tube. 

There would be a massive muzzle blast when the rocket exits the launch tube. Therefore, some form of muzzle silencer would be required. 

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