War Theory: A Technical Analysis of War of the Worlds [Part 2]09 May 2017 0
"No one would have believed in the last years of the nineteenth century that this world was being watched keenly and closely by intelligences greater than man's and yet as mortal as his own; that as men busied themselves about their various concerns they were scrutinised and studied, perhaps almost as narrowly as a man with a microscope might scrutinise the transient creatures that swarm and multiply in a drop of water. …Yet across the gulf of space, minds that are to our minds as ours are to those of the beasts that perish, intellects vast and cool and unsympathetic, regarded this earth with envious eyes, and slowly and surely drew their plans against us. And early in the twentieth century came the great disillusionment.” – War of the Worlds
Part II – Reverse Engineering the Martian War Machine – Power to Weight Ratios and Movement
Martian war machines were 30-meter high tripods. The top 3 meters (10 feet) consisted of an enclosed cowling that housed the operator, along with its (his? her?) instrumentation and equipment, power plant and environmental controls. The legs of the tripods measured 27 meters (90 feet) in length with their movement while walking potentially affecting the height of the war machine and the elevation of the occupant inside.
Actual movement of the tripod's legs were a more fluid version of a man on crutches (2 legs, then 1 leg, then 2 legs then 1 leg, etc.). The closest living analog would be a more graceful three-legged dog. The estimated power plant would certainly be sufficient to provide enough energy for movement at speeds of up to 60 miles per hour (96.5 kph) - the tripods are described as moving at a speed equivalent to a fast locomotive in Wells' day. By comparison, the top off-road speed of an M-1 Abrams tanks is half the speed of a Martian tripod (only 30 mph). However, that fact that the Martians' heat ray requires such a huge amount of energy would explain why the tripods must stop to fire, they probably didn’t have enough energy to move and fire simultaneously.
Their length of stride would be limited by the need to maintain a stable posture with the angle between the legs no more than 60 degrees (or 30 degrees to the vertical). In this position, each leg (or pair of legs) would form the hypotenuse of a triangle with the adjacent segment being the vertical and the opposite segment being the ground surface. With the sin of 30 degrees being 0.500, each step would be equal to 90 feet (2 x 0.500 x 90 feet). A speed of 60 mph is equal to 1 mile per minute, or 88 feet per second. Therefore, when moving at top speed, a tripod would have to take a stride every second.
The leg movements themselves are complicated by the need to maintain an even elevation for the tripod’s operator. At midstride, with all the legs in alignment the cowling would be at its maximum height of 90 feet. However, the cosine of 30 degrees is 0.866 the height of the cowling would fall to approximately 78 feet (24 meters). That’s a rise and fall of 10 feet (3 meters) with each step, which occurs every second at top speed. The occupant could not be subject to such shaking, in effect being dribbled like a basketball to heights of ten feet, especially on a plant whose gravity is 2.5 time greater than the operator’s home world. Therefore, the legs themselves must change length while walking, being shorter at mid stride and longer at the end of the stride to keep the cowling and its occupant level. This could be done by segmented legs that bend further as needed to achieve the required length, telescoping legs the extend and contract during movement, or curled legs that wind and unwind with each step. However, no detailed description of this movement is given.
The cross section of the leg struts themselves would best be circular. The tripod will be constantly changing direction and speed, and a circular cross section does not present a directional and variable moment of inertia (like an I-Beam would, for example). Which brings us to the applied loads on the leg struts and the question of how much a tripod weighs.
The cowling’s superstructure is described as being as big as a one-story house. House movers will transport loads between 80,000 and 160,000 lbs. Assuming a small house of 100,000 lbs what would be the equivalent weight of such a structure made from more advanced material than pine wood framing (pine having a density of 0.54 g/cc)? There are two potential materials that could be used to construct the tripod, traditional carbon steel (7.7 g/cc, 15 times the density of wood) and more advanced carbon fiber composites or even nanotubes (1.56 g/cc, 3 times the density of wood). Assuming the same ratio of shell/wall and interior structure to open space as the house being used as the baseline (Martian bodies/heads are exceedingly large and there will be the need for control equipment and instrumentation). In round numbers, a carbon fiber cowling would weigh approximately 300,000 lbs, while the steel version would weigh 1,500,000 lbs.
However, the main load would be the tripod’s power plant. As mentioned before this would be equivalent to a 200 Mw small modular reactor. These vary in size, weight and dimension but an average weight of 500 tons (when loaded with fuel rods) can be assumed for the power plant. This adds another 1,000,000 lbs. to the weight on the legs. So, the total weight of the carbon fiber cowling would be 1,300,000 lbs. (almost 600,000 kg) and the steel cowling would be 2,500,000 lbs. (almost 1,200,000 kg). So, again in round numbers, each leg would carry about 200,000 kg if made of carbon fiber and 400,000 kg if made of steel.
Note: I am making some simplifying assumptions here. As the legs move from a vertical upright positon to a complete stride, the weight loadings of the cowling and the reacting loads on the leg’s feet would become oblique instead of axial, inducing further bending moments in the legs. Also ignored are concentrated point loads at bending joints or the additional weight from leg extension machinery.
Also, the only military action taken by Martian flying machines was the spreading of poisonous gas. At a weight of 500 tons, the power plant needed for the heat ray would have been too heavy to mount on an aerial platform.
We can now estimate the diameter of each leg using a buckling formula for column loadings. This formula is gives the relationship between the applied weight load and the following: the length of the leg, the leg’s internal strength characteristics (as defined by the material’s modulus of elasticity) and the geometric moment of inertia defined by the leg’s cross sectional area. The strength modulus of advanced carbon fiber nanotubes is estimated to be about 138,000,000 psi (950 GPa) while steel has a modulus of 29,000,000 psi (200 GPa) – making carbon fiber nanotubes 23.5 stronger per unit weight than steel. Arranging the formula to determine the required cross sectional moment of inertia, carbon steel would require 1580 in^4 – a circle with a radius of 45 inches (1.14 meters, a cross sectional area of 4.08 meters^2). The carbon nanotubes would require only 166 in^4, or a circular radius of 14.5 inches (0.37 meters, a cross sectional area of 0.43 meters^2). A steel construction is not practical.
The additional volume of each carbon nanotube leg would be 11.61 cubic meters. At a density of 1.56 g/cc (1560 kg/M^3) each leg would weigh 18,112 kg or over 54,000 kg total. With the cowling and power plant’s estimated weight of 600,000 kg, along with other equipment, furnishings, appurtenances, weapons (gas canisters, tube gun and the heat ray projector), the total weight of a Martian tripod could be approximately 700,000 kg (1,543,000 lbs or 772 tons). Its 200 MW power plant would generate 268,200 HP, giving a power to weight ratio of almost 350 HP/ton. By comparison, an M-1 Abrams tank weighs 62 tons and is equipped with 1,500 HP engine giving it a power to weight ratio of 24.2 HP/ton. Clearly the Abrams is out classed.
Lastly there is the issue of the feet. During its stride, the tripod balances one either one or two legs as it advanced forward like a man on crutches. At some point in this cycle either its entire weight or half of its weight is being transmitted through the legs and into the ground below. The bearing capacity of the soil therefore becomes a critical concern. This can vary from 33 kg/cm^2 for hard rock to 0.5 kg/cm^2 for soft clays. At the maximum one legged load of 700,000 kg, walking on rock would require a circular foot pad of 21,212 cm^2 (a radius of 82 cm, or a diameter of 1.66 meters). To navigate the other extreme, soft clay soils, its foot pad area would have to be 1,400,000 cm^2 (a radius of 667 cm, or a diameter of 13.3 meters – probably too large for practical movement.
While a tripod would certainly have the power to pull its legs out of the muck, this does illustrate that it has certain terrain limitations. Wet and marshy conditions are something not encountered on a desert planet like Mars. It seems that a strong rainstorm would be better at slowing the Martian’s advance than any Royal artillery battery. So, any Human survivors of a successful Martian invasion should hold up in jungles, marshes and peat bogs – instead of the London sewer system. What is left of Human civilization could possibly survive in the heart of the Amazon or the Congo.
If you do manage to survive the Martian invasion, make sure to tune in next week for Part III, where we examine the logistics and economics behind a planetary invasion.