The Mathematics Behind Why Rockets Can Escape The Gravitational Pull of the Earth

Konstantin-TsiolkovskyRobert Goddard’s liquid rocket never reached the 3 kilometer mark because of Tsiolkovsky’s Rocket Equation named after Soviet scientist Konstantin Tsiolkovsky (pronounced “con-stan-tyin tsel-kov-skee”). This equation states that as fuel increases for faster and further voyages, so too does the weight, becoming increasingly heavy as more and more fuel is added. Tsiolkovsky took into account the velocity of a rocket alongside its mass of payload, mass of fuel, and the mass of the rocket itself. The longer the engine burns, the more velocity the rocket will have, however longer burning means more fuel which adds weight and makes it more difficult to push upwards. To travel fast enough to deliver a rocket to space, most of the craft must be fuel. Scientists have battled with this question for decades and although mathematical constructs have been developed to explain the relationship between weight and thrust, no one has yet to develop an idea to get around this problem with currently available technologies. The equation developed to explain this limitation of space travel is △V^R = V^E x log^e (M^P + M^F + M^R / M^P + M^R). This effectively states that only a tiny portion of a rocket can be used to deliver payload, with notable cases being the Apollo missions which employed enormous rockets to carry just a few small astronauts and the things they needed into space. Tsiolkovsky theorized this in the beginning of the 20th century as his calculations demonstrated that kerosine wouldn’t be enough to go from the Earth to the moon with a single craft

Super Mario’s Super Human Jumping Capabilty

Super-Mario-jumping

The Nintendo mascot Mario has a vertical jumping range of 11’5” within his own world which equates to 27’ upon Earth as Earth has a different gravitational pull than that of Mario’s world. Mario is capable of leaping 2.25x his own body height however his exact agreed upon height when converted to a real world measurement is unclear. Statues erected of Mario tend to be 4’10” – 5’1” in length and Nintendo has stated that Mario’s official height is in fact 5’1” however different video games portray Mario with a varying degree of physical characteristics (e.g. height, weight, speed etc.). Mario falls back down to the ground within 0.3 seconds of his take off which means that the gravitational pull of his fictional world is 8x stronger than the gravitational pull of Earth. If this world were physically real, Mario would need to have legs powerful enough to allow him to jump at a speed of 22.2 meters per second, an incredible feat of physical prowess as the average person standing upon the Earth is only able to jump at a rate of 2.24 meters per second, resulting in an almost 10x difference in terms of Mario’s physical capabilities to that of a typical human being

Robert Goddard’s Liquid Fueled Rocket Concept

Robert-Goddard

Robert Goddard devised the idea of liquid kerosene and liquid oxygen being mixed together to create a fierce, but most importantly, a controllable flame for propulsion. When kerosine reacts with oxygen, the result is an incredibly hot, rapidly expanding gas which when channeled through a nozzle, creates enormous thrust. On March 16, 1926, Goddard launched the world’s first liquid fuel rocket bearing this concept. This rocket did not travel fast nor far but it did demonstrate a proof of concept making space flight theoretically possible for the first time in human history

Stealth Aircraft Technology

stealth-aircraft

Stealth aircraft are shaped and angled as such so that any signal bounced off of them bounces in a direction different than that of how it came in making Radio Detection and Ranging or Radio Direction And Ranging (RADAR) unable to ping and receive a signal back which makes stealth aircraft essentially invisible as they cannot be seen with the naked eye due to the incredible speed and height at which they travel, nor can it be tracked with technology

Aircraft Carriers

aircraft-carrier

Landing an aircraft on an aircraft carrier at sea is considered the most difficult task in aviation. The first aircraft ever landed on the deck of a steamship was accomplished in 1911, just a few short years after the Wright brothers had the first airplane become airborne. The task was accomplished by having ropes and sandbags run horizontally across the wooden landing stage on top of the deck of the ship. The rope caught a hook on the bottom of the landing aircraft and slowed it down, with each bag adding more and more weight. The engineering of this practice is still in use today, with the only significant difference being the components used, which are now high tension steel cables. Navy Marines and other ranked Navy and Airforce officers jointly train for their wings, but Navy Marine officers are more likely to take off at sea, whilst Navy officers are more likely to take off from land

Challenger Spacecraft

cement-and-concrete

The reason the Challenger space craft exploded 73 seconds into its launch on January 28, 1986 was because the temperature the morning of the launch was -1 degrees Celsius which caused the o-rings placed around the rocket’s boosters to shrink and leak fuel upon liftoff. This theory was brought to light by Valentina Tereshkova, who was the first woman in space. Tereshkova relayed her theory to one of the heads of staff at the National Aeronautics and Space Administration who then relayed it to Richard Feynman by showing him how vehicle carburetors which also have o-rings experience the same issue. If the ambient temperature is below 11 degrees Celsius this issue is a common occurrence with all o-rings, regardless of the vehicle or craft it is installed upon

Aircraft

aircraft

At any given time there are approximately 1,000,000 (1 million) people worldwide upon aircraft which are actively flying. The average commercial passenger aircraft weighs 100 tonnes, lands on a runway 150’ wide, and lands at 240 kilometers per hour whilst dropping at a rate of 10’ per second. Approximately 100,000 flights occur daily worldwide. Rolls Royce aircraft engines travel 16,000,000 (16 million) kilometers in between servicing and as such, they have sensors which send wireless data in real time as an aircraft is airborne. Most aircraft and their engines now employ this technology behind the scenes as a safety measure to ensure every flight goes smoothly. There are approximately 35,000 parts in each aircraft engine. Aircraft engines spin at 150 revolutions per second making them spin 9000 times per minute. Statisticians estimate that flying is up to 50x more safe than driving a vehicle. Approximately 7 in 1000 luggage bags do not meet their destination on time and approximately 1,400,000 (1.4 million) luggage bags per year never reunite with their owners due to lost tags or abandonment. Unclaimed luggage eventually goes to auction due to space requirements. Approximately 50% of every aircraft can be reused and the other 50% can be recycled. The most expensive and sought after parts to reuse are the engines and the most expensive and sought after parts to recycle are aluminum