Can We Solve the Big Problem with Rocket Launches?

The simple rocket equation shows why a single stage rocket to space is incredibly difficult.

Every rocket used to carry payloads into Earth orbit today uses the multistage principle. Two or more rocket stages, stacked vertically and sometimes aided by strap-on boosters will fire, burn and then are dropped off to lighten the weight for successive stages to accelerate the payload to the 17,000-plus miles per hour needed to sustain orbit. But why not simply use one stage? A simple mathematical equation called the rocket equation shows that the weight penalty of carrying the quantities of fuel and oxidizer necessary to lift the entire mass into earth orbit is prohibitive, and propellant burn alone is not enough to lighten the structure sufficiently. But there is hope for a high-tech solution that may change everything.

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Launching payloads into orbit has always been difficult. As a species, we have only been doing it for 65 years, and it’s always been expensive and difficult.  

One of the reasons why it’s so expensive is because of the need to use composite rockets consisting of two or more separate rockets stacked together as stages, dropping off lower stages as the assembly accelerates to the over 17,000 miles per hour needed to sustain Earth orbit.  

Ever wonder why we can’t just build one giant rocket with powerful engines and simply blast the entire thing straight into orbit? The answer is found in remarkably simple mathematics called the rocket equation. It was derived by the Russian Konstantin Tsiolkovsky at the turn of the last century, decades before spaceflight was even close to a practical reality—so this was developed from first principles, not empirically. It is rooted in the basic equations of Newtonian physics, and it’s immutable.  

The key thing to notice about the rocket equation is that the velocity term on the left—the speed needed to reach orbit—is solely dependent on two variables on the right: engine exhaust gas velocity and the ratio of full to empty weight of the rocket. Engineers call this the mass fraction, and structurally, this is the core of the single-stage-to-orbit problem.  

The velocity needed to attain orbit is naturally a constant, and exhaust gas velocity available through the combustion of chemical rocket tops out at something a little less than three miles per second, about 6,500 miles per hour. I’ll spare you the mathematics, but with a fixed exhaust gas velocity and a known orbital velocity requirement, the mass fraction needed for single stage to orbit could be as high as 40 to 1. And since the only way single stage to orbit rocket can reduce its mass in-flight is to consume propellant, very little of the launch weight of the vehicle can be made up of engines, tanks and airframe.  

Structure is heavy. There is just no way around this problem. So, to solve it, as the rocket lifts off and flies, its mass has to drop by more than just the weight of consumed propellant and oxidizer. That’s why rockets are built in stages, so that dropping off the dead weight of empty tanks, airframe and engines allows the now smaller rocket to ignite and start it’s part of the journey not only higher but faster, lowering the necessary delta V to reach orbital speed.  

Two stages are common, but as many as four have been used for satellite launch. Is there any way to get around this seemingly impossible restriction on single-stage-to-orbit? Possibly, but it will take some engineering.  

A British company called Reaction Engines is building a new type of powerplant that uses a combined cycle, a novel air-breathing ramjet that transforms into a rocket once the aircraft has reached high altitude and hypersonic speed, to continue his journey into space. With advanced materials and high-performance propellants like liquid hydrogen, it is theoretically possible to achieve single stage to orbit, but to do so carrying any useful payload is doubtful.  

Has anyone come close? Yes, ironically a long time ago. In December of 1958, a test version of the Atlas ICBM was launched into orbit carrying a recorded Christmas greeting from then-President Dwight Eisenhower. The Atlas was considered a one-and-a-half stage rocket, because it dropped two of its three engines in-flight, but achieved orbit with the launch tankage and airframe. Even then, to pull off a mass fraction that works with the rocket equation, the engineers that designed it at Convair had to eliminate the conventional rigid airframe construction and build the Atlas out of paper-thin stainless steel, inflated with nitrogen gas like a giant balloon.  

This expensive and difficult to handle technology resulted in a rocket with a mass fraction of a little over 20, a figure that has not been improved on today. Atlas would go on to a long and storied history as the launcher for John Glenn and the Mercury astronauts as well as interplanetary space probes, but to lift any real weight into orbit even it needs a second stage.  

Propulsion is a problem. Nuclear rockets could be a solution, but there are obvious drawbacks to flying reactors. The Reaction Engines hybrid engine approach looks promising but has been decades in development. And I doubt that airframes and tankage can get much lighter than they are now.  

Does this mean that we are never going to board a space liner and fly into orbit like Kubrick’s 2001: A Space Odyssey? Not with chemical rockets, but maybe with hybrids. Hybrids are the hottest thing in the automotive industry now, so why not rockets?

Written by

James Anderton

Jim Anderton is the Director of Content for ENGINEERING.com. Mr. Anderton was formerly editor of Canadian Metalworking Magazine and has contributed to a wide range of print and on-line publications, including Design Engineering, Canadian Plastics, Service Station and Garage Management, Autovision, and the National Post. He also brings prior industry experience in quality and part design for a Tier One automotive supplier.