A Proposal to Reduce the Delta-V to Orbit.

To reach orbit you have to have your vehicle have a horizontal, i.e., tangential, orbital velocity, of about 7,800 m/s and have sufficient altitude, say at least 100 km, the altitude considered to be "space" (1) NO, altitude and velocity are related one to the other, the higher the velocity the higher the altitude! This is given by the equality between attraction and "centrifugal force" at the given altitude. (1) To get to this altitude you have to have a separate velocity in the vertical direction. The usual way to estimate this vertical velocity is by using the relation between kinetic energy and potential energy. It gives the speed of v = sqrt (2gh) to reach an altitude of h meters. At 100,000 m, v is 1,400 m/s. So then it is common to estimate the required delta-V to orbit to be 1400 + 7800 = 9,200 m/s. However, it seems to me you can reduce this by traveling in a straight-line path. (2)Oh yes BUT you do not have at the end the tangential speed to stay in orbit! One of the reasons to have launch pads near to the equator is to gain the earth speed which is maximal at this latitude (0°).(2) If you travel at an angle to the horizontal so that your vertical velocity component is 1,400 m/s and your horizontal component is 7,800 m/s then you only actually need sqrt(7800^2 + 1400^2) = 7,925 m/s delta-V. Actually if you add on the ca. 460 m/s velocity you get for free from the Earth's rotation you might be able to reduce this to sqrt(7400^2 + 1400^2) = 7,531 m/s. So what I'm trying to investigate is if it is possible for a rocket, without using wings or lifting surfaces, to travel at such a straight-line trajectory at an angle from lift-off so that the achieved velocity will be in this range. The question is: if you angle the rocket from the start with the thrust vector along the center line with the trajectory angle such that the vertical component of the thrust equals the rocket weight could you have the rocket travel at a straight-line all the way to orbit? I'm inclined to say no because the gravity is operating at the center of gravity of the rocket not at the tail where the thrust is operating. This would certainly work if you had a point particle, but I'm not sure if it would work when your body has some linear extent. (3)It is right that gravity acts in COG. But the force from the jet(s) is axial so that both forces do meat (their acting direction do cross in the COG) so that it is possible to consider them as acting on a point. The "non crossing" can be compensated by a jet slight angle. This is done with gimbal cylinders you surely have seen.(3) This method for traveling at a straight-line at an angle for some or all of the trip would make my calculations easier. However, I'll show in a following post there is another way to do it even if this first method doesn't work. The second method though would require some modification to the usual design of rockets and is more computationally complicated. The question I'm asking can be boiled down to this: imagine you have a long cylindrical object, could be a pencil, could be broom stick. You can give it an initial thrust at the bottom and push it away at an angle. It will then follow a curved trajectory with its center of mass following a parabolic arc, disregarding air drag. Then what I'm asking is will it work to supply a continual push at the bottom with the force maintained at the bottom at a fixed angle to the horizontal so that the vertical component of this force is the cylindrical body's weight? Will the body maintain a continual straight-line trajectory at this set fixed angle? (4)In fact there is no need for a straight trajectory but for the one which brings the object to the needed speed at the right height and with the lowest energy.(4) This is really actually a question in continuum mechanics, sometimes called solid mechanics. In physics we often idealize a body subject to forces as a point particle. Idealized this way, the thrust force applied to the rocket would add as a vector to the force of gravity so it would cancel gravity no matter what the angle of the trajectory. (5)NO, NO and again NOOOO it is not a "continuum mechanics problem since the body you try to move is finite as dimension.(5) But in continuum mechanics you have to consider the physical extent of the body and where on the body the forces are applied. I imagine this is a common type of problem addressed in mechanical engineering and civil engineering. (6)This is a COMMON problem for mechanics a problem of BODY mechanics not CONTINUUM mechanics.(6) A force applied at one position on the body won't have the same effect as when it is applied to another point for instance in regards to the torque produced. Torque is measuring the turning "force" on the body. But it's defined as the cross product of the force vector times the radial vector to the center of rotation. (7)Correct valid for any BODY(7) Intuitively, what we have to worry about is rotation of the rocket with the thrust applied only at the tail. But if the rocket were to rotate it would be about the center of gravity. However, if we make it so the thrust is always along the center line, the radial vector to the cg and the force vector are parallel, resulting in a 0 torque vector. (8)Between 2 parallel vectors there is a lever arm thus a torque!(8) That would mean there would be no rotation around the center of gravity so we should be able to maintain our straight-line trajectory. This would be valid if the center of gravity were fixed. But the cg is accelerating as the thrust is applied. (9)You unfortunately mix notions, I would suggest, since you have ideas, to take again a good book about mechanics and review.(9) So I'm not sure if this argument applies in that case. Bob Clark (10)Sorry with the access I have I only could separate my comments from your text but could not make them bold or underline. there are (9) comments + this one.(10)

Hi Nick Name,

I have found that I have to write everything out first and then select the text I want to format. If I have nothing selected, the text formatting functions are disabled. I am using Firefox. What browser are you using?

Mike

Nick Name said:

(4) This is really actually a question in continuum mechanics, sometimes called solid mechanics. In physics we often idealize a body subject to forces as a point particle. Idealized this way, the thrust force applied to the rocket would add as a vector to the force of gravity so it would cancel gravity no matter what the angle of the trajectory. (5)NO, NO and again NOOOO it is not a "continuum mechanics problem since the body you try to move is finite as dimension.(5) But in continuum mechanics you have to consider the physical extent of the body and where on the body the forces are applied. I imagine this is a common type of problem addressed in mechanical engineering and civil engineering. (6)This is a COMMON problem for mechanics a problem of BODY mechanics not CONTINUUM mechanics.

OK. Call it "rigid body dynamcs".

My question is this: if you apply a force on a cylindrical body at the bottom at an angle in such at way the force vector goes through the center line and so that the vertical component of the force cancels or exceeds gravity, can the body travel in a straight-line?

Bob Clark

some ideas that have already been looked at in this vein:

Gerald Bull's classic "supergun" which uses a long straight tube filled with a mixture of hydrogen and oxygen with ceramic burst disks at each end. a light gas gun is fitted to one end to inject a projectile with a special shape through the first burst disk. the shape is designed like the throat of a scramjet such that it compresses the hydrogen/oxygen in the annular space between the pipe and the projectile and causes it to burn across the back side of the projectile which is shaped like the spike of an aerospike rocket engine. the longer the tube, the faster the projectile can go. it can theoretically accelerate a projectile to escape velocity and beyond. NASA has contemplated using it for unmanned launches (due to the extreme g-forces possible.) Shortly before his death Gerald Bull was working with Saddam Hussein to build project "Babylon" which was intended to launch payloads at Israel or at satellites. This is also known as a ram accelerator. Using H2/O2 as the gas mixture 8000m/s muzzle velocities are theoretically possible using this method.

http://www.fas.org/nuke/guide/iraq/other/supergun.htm

http://en.wikipedia.org/wiki/Light_gas_gun

http://en.wikipedia.org/wiki/Project_Babylon

http://en.wikipedia.org/wiki/Ram_accelerator

there is also a concept for a electromagnetic catapult similar to a maglev train, but it would probably be unable to get out of earths gravity well but may work well on the moon or mars.

http://en.wikipedia.org/wiki/Mass_driver

There are other concepts like space elevators and skyhooks and similar things but they require materials with properties unobtainable as yet, at least for an earth gravity well. but they are currently possible on the moon or mars.

http://en.wikipedia.org/wiki/Non-rocket_spacelaunch

One other point about your straight line trajectory, using that trajectory, you spend entirely too much time in the atmosphere generating drag and stress on the airframe. The shuttle has to throttle back it's engines for a time at about the midpoint of it's ascent because the acceleration rate is such that if the engines continued at full throttle, the airframe would disintegrate due to the aerodynamic loading. It is a performance region called "max-Q". conventional rockets either go straight up until they get above most of the atmosphere and then they begin to arc over to minimize the aerodynamic loading, or they piggyback on a mother-ship aircraft to a very high altitude before they start their ascent, that way by the time they have accelerated to a point where aerodynamic loading could be a problem, they have gained enough altitude that there isn't enough air to be a problem.