Some people get very excited about the possibilities of warp drives for spacecraft. They discuss the concepts of powering a spacecraft using the distortion of space-time in front and back of the craft. This Popular Science article talks about the technical aspects of the theoretical drive mechanisms. I wondered how much readers knew about warp speed and how it is calculated. I won’t go into detail about the physics since it is hypothetical. I only practice physics of the real world. Instead, I refer you to the concept in Star Trek for all the jargon you might want to see.
Warp drive is a hypothetical faster-than-light (FTL) propulsion system in the setting of many science fiction works, most notably Star Trek. A spacecraft equipped with a warp drive may travel at apparent speeds greater than that of light by many orders of magnitude, while circumventing the relativistic problem of time dilation. In contrast to many other fictional FTL technologies, such as a “jump drive” or the Infinite Improbability Drive, the warp drive does not permit instantaneous travel between two points
First, I must offer this disclaimer. I am not a Trekkie. Although, I do live 12 miles from the future boyhood home of James T. Kirk in Riverside, IA. What I offer here is strictly from internet sources. So, it is guaranteed accurate and correct. Sure it is. According to the Star Trek Technical Manual, a warp factor is a simple mathematical calculation. Your speed ν is a factor of the speed of light c. The factor is ω called warp factor. The value is cubed. Warp 1 is 1x1x1xc. Speed v = c. For Warp 2 you get 2x2x2xc or 8c, 8 times the speed of light. FYI…In the 23rd century, warp factors of 10 and higher were known as generally unsafe velocities.
A bit of algebra allows rearrangement of the equation for a calculation of ω.
So, that’s it. Warp factor is nothing special. All you need to know is your speed relative to the speed of light. Divide and take the cube root. Voila…ω. If you are really interested in more…
In the Real World…
NASA reported very recently that the Dawn spacecraft left the asteroid Vesta on the next phase of the mission to take it to the largest asteroid Ceres in February 2015. One thing which makes Dawn unique is its rocket propulsion engine. Dawn uses an Ion Engine, not a conventional combustion engine. Dawn was placed into Earth orbit in September 2007. Conventional rockets placed it in Earth orbit with a speed relative to the surface of about 7,800 m/s. For those not familiar with the metric system, that is nearly 5 miles/sec. Dawn then needed to increase its speed to 11,000 m/s in order to move away from Earth and proceed on an interplanetary journey past Mars and then to Vesta and Ceres. It used its ion engines for thrust. The graphic below shows the ion engine operation times. Blue is engines thrusting. Red is coasting with engines off.
What about Dawn’s warp factor? That’s easy to show. It reached a speed of 11,000 m/s compared to light speed of 300,000,000 m/s. So…
Not such a big deal, is it? Why use an ion engine for this spacecraft? What is the advantage?
Ion Propulsion Engines
Ion engines are about ten (10) times more efficient than conventionally fueled engines. This NASA graphic illustrates it. Dawn has a low thrust value of 90 milli-Newtons. This is comparable to the force exerted by a single sheet of paper resting on the palm of a hand. It can exert this thrust for very long periods of time. It uses much less fuel to achieve the same change in speed as a chemical rocket. Chemical rockets fire for brief times, but consume large amounts of fuel.
The key to this difference in efficiency is due to the speed of the escaping gases at the engine nozzle. Chemical rocket exhaust speed is around 4,000 m/s. Ions escape from the nozzle at speeds approaching 40,000 m/s. This can be illustrated by the following analogy. Stand on a low friction skate board. Aim a low powered repeating BB gun horizontally so you will roll away from the direction of the fired BBs. Fire off a few seconds of BBs. You won’t go backward very fast. Replace the BB gun with one that weighs the same but fires high speed BBs. The faster the speed of the exhausted BBs, the faster you will recoil the opposite direction.
Ion engines deliver much faster exhaust speeds, and can fire for prolonged times. They deliver changes in speed much greater per kg of fuel than conventional chemical rocket engines. This is called Specific Impulse. For more details about specific impulse, follow this link.
Historically, ion engines have been developed over the last 50-60 years. The principle behind the ion engine is akin to removing socks out of the clothes dryer on a dry day. The sox repel each other because they are electrostatically charged. Like charges repel. Ion engines charge a fluid so its atoms can be expelled in one direction out the nozzle and drive the spacecraft in the other direction. Dawn’s ion engine uses xenon gas that is more than 4 times heavier than air.
When the ion engine is running, electrons are emitted from a hollow tube called a cathode. These electrons enter a magnet-ringed chamber, where they strike the xenon atoms. The impact of an electron on a xenon atom knocks away one of xenon’s 54 electrons. This results in a xenon atom with a positive charge, or what is known as an ion. At the rear of the chamber, a pair of metal grids is charged positively and negatively, respectively. The force of this electric charge exerts a strong electrostatic pull on the xenon ions. The xenon ions shoot out the back of the engine at a speed of 100,000 km/h (60,000 mph). At full throttle, the ion engine will consume 2,500 watts of electrical power, and put out 1/50th of a pound of thrust. That’s far less than the thrust of even small chemical rockets. But an ion engine can run for months or even years, and it’s up to 10 times more efficient. In June 1996, a prototype engine built by NASA/Lewis began a long-duration test in a vacuum chamber at JPL simulating conditions of outer space.The test concluded in September 1997 after the engine successfully logged more than 8,000 hours of operation.
I hope you have a better appreciation of the concept of warp factor and the current state of some high technology of rocket propulsion. Someday we may realize the dream of warp drives. Until then, more research and development is needed.
Thank you for reading…JAR