The following is an attempt to analyze the trip made by the Anacreontian fleet in "The Mayors" (3rd part of "Foundation"). The resulting power generation figures are the highest I have calculated so far from reading Asimov's books, excluding the contested planet blowing statements.
Unfortunately, considering my high school level knowledge of physics, I wouldn't be surprised if I have made some mistakes, so I ask those better prepared than I to check my numbers and tell me anything wrong they might find.
Trip of the Anacreontian fleet to Terminus.
Situation: The Wienis (old Imperial battlecruiser) and the rest of the Anacreontian fleet are heading for the edges of Anacreon star system in order to jump for Terminus. About this, prince Wienis (the instigator of the attack) states:
Relevant information:Prince Wienis wrote:"If you're really interested, the ships of the fleet left Anacreon exactly fifty minutes ago, at eleven, and the first shot will be fired as soon as they sight Terminus, which should be at noon tomorrow. You may consider yourself a prisoner of war."
1) It is a well known fact that Foundationverse ships need to travel far from stellar gravity wells in order to jump. Jumps made within gravity wells (such as that made by Lathan Devers above Trantor in Foundation and Empire) are extremely erratic. Even the far more advanced Far Star 2 (a "gravitic" warship that sported a state-of-the-art computer produced by four centuries more advanced Foundation technology) needed to travel roughly 1.500 million kilometers away from Comporellon's star (Foundation and Earth) in order to make an accurate jump.
2) The Terminus-Anacreon route was well known at this time. It can be supposed that there were well known jump points from where a direct jump into Terminus system is possible. This would allow the Anacreontian fleet to jump inmediately without the well known delay needed to calculate a jump under many other situations. Alternatively, the calculations might be simpler than usually and the span of time required might be shorter.
3) Wienis might be using Anacreontian local time, but this wouldn't completely invalidate the calculations. Anacreon's description is that of a normal Earth-like planet and, thus, its rotation movement can't be a lot different from that of Earth. Its day might be slightly shorter or slightly longer than Earth's, but standard time units (AKA Earth time) should still be a decent average.
4) I found this formula in the Power technologies section of the SWTC and it is what I used for my calculations.
Data:Curtis Saxton wrote:The kinetic power of a ship pushed by a relativistic particle stream is approximately P = F c, where F is the thrust (force, in Newtons) and c is the speed of light. If the mass of the ship plus its fuel is m and the acceleration is a then we simply have F = m a, which is familiar to students of Newtonian physics.
Known length of the Imperial battlecruiser: 2 miles (roughly 3 km).
Top time that the trip might have taken: 13 hours.
Low-end figures:
Supposing the Imperial battlecruiser to be a cylinder with a 100 m in diameter, as dense as air, and needing the 13 hours to travel from Anacreon (we shall suppose that Anacreon is as distant from its star as Earth from the sun) to a point as distant as Mars.
Data:
Volume of the Imperial battlecruiser: 2.35E7 m^3
Density of air: 1.29 kg/m^3
Mass of Imperial battlecruiser: 3.03E7 kg.
Average distance (Earth-Mars): ~75 million km.
Average speed (supposing continuous acceleration throughout the thirteen hours): 1602 km/s
Final speed (supposing initial speed 0): 3205 km/s
Acceleration: (Final speed - Initial speed)/time = 0,068 km/s^2 = 6.98 g.
Power: F * 3E8 m/s (speed of light) = (3.03E7 * 68.48 m/s^2) * 3E8 m/s = 6.22E17 w = ~148 megatons/second.
Average figures:
Supposing the Imperial battlecruiser to be a cylinder 250 m in diameter, with average density equal to that of water and needing seven hours to travel from Anacreon (we shall suppose that Anacreon is as distant from its star as Earth from the sun) to a point as distant as Saturn.
Data:
Volume of the Imperial battlecruiser: 1.47E8 m^3
Density of water: 1000 kg/m^3
Mass of Imperial battlecruiser: 1.47E11 kg.
Average distance (Earth-Saturn): ~1300 million km.
Average speed (supposing continuous acceleration throughout the seven hours): 51587 km/s
Final speed (supposing initial speed 0): 103174 km/s
Acceleration: (Final speed - Initial speed)/time = 4.09 km/s^2 = 417.77 g.
Power: F * 3E8 m/s (speed of light) = (1.47E11 * 4094.23 m/s^2) * 3E8 m/s = 1.805E23 w = ~43 teratons/second.
High end figures:
Supposing the Imperial battlecruiser to be a cylinder 600 m in diameter, with average density equal to that of iron and needing three hours (we shall suppose that over half of the thirteen hours are needed to calculate the jump to Terminus) to travel from Anacreon (we shall suppose that Anacreon is as distant from its star as Earth from the sun) to a point as distant as Saturn.
Data:
Volume of the Imperial battlecruiser: 8.48E8 m^3
Density of water: 7870 kg/m^3
Mass of Imperial battlecruiser: 6.67E12 kg.
Average distance (Earth-Saturn): ~1300 million km.
Average speed (supposing continuous acceleration throughout the three hours): 120370 km/s
Final speed (supposing initial speed 0): 240740 km/s
Acceleration: (Final speed - Initial speed)/time = 22.29 km/s^2 = 2274.57 g.
Power: F * 3E8 m/s (speed of light) = (6.67E12 * 22290.8 m/s^2) * 3E8 m/s = 4.46E25 w = ~10 petatons/second.
Comments? Critics? Please, go easy on the flames.