Explaining Potential Energy

For some reason I get asked on this a lot, it seems not many people are as smart or were taught as much as I was. That being said, I didn't know what the actual word "potential" was until basically 9th grade, but I did know what potential energy was by third grade because I had nothing to do and stared at my bedroom ceiling when bored due to my brother hogging the one and only family computer / game console, though mind you at this age most of my class couldn't even spell big words like "orchestra" so I don't see why half of humanity still doesn't understand these basic physics concepts as adults. You don't need fancy numbers for this shit. Screw textbooks, and thus why you are probably here.

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Potential energy can mean several different things. Knowing what potential energy can save your life, whether it be in an aerial dogfight or being an electrician, or even just driving a car and knowing why you shouldn't speed down steep hills.

Potential energy, is the energy (unit is force multiplied by distance and mass of the objected in relation) difference (they use mathematical delta Δ for this as you can get it by triangulating between two points on a two dimensional graph) between two states.

I will expand upon these examples below but here are a few short examples:

• • Voltage is like the eagerness for electrons to move some quantity from one area to another area. The two points don't have to be related to each other, the electrical energy just has to be compared to each other. and you can get a number. A volt meter can work by connecting  an extension of these two points close to each other and sticking a poor dude in the middle and see how far one side pushes him and the other side pulls him there, while a current meter allows a tiny bit of current through to count how much passes through and is kind of like an electron counter of sorts.

  • Height potential energy generally refers to the eagerness for something to basically fall down if left untouched to the lower state due to gravity, which is why a lot of people use the ball on the hill example. Lower usually implies closer to a big fucking mass such as the earth, which is why the earth is also round because it's stuck together with gravity, but it doesn't have to specifically relate to the earth, but we don't general deal with problems such as apples attracting to each other as earthlings due to friction. Height potential energy doesn't have to specifically relate to gravity either because it can be used with other examples such as electrical repulsion and attractance. With repulsion, you just inverse the number sign (+/-) as the objects get closer if you actually end up doing the maths.

Electrical Voltage

For fucks sake, why are people even using the ball on the hill and pipes for this analogy, it doesn't explain jackshit, so I've got two examples here, a theoretical scenario and the country migration example.

Voltage is the potential energy, or eagerness or state of electrical charge difference between two points. Current is how much shit is being transferred between the two points. You can't have a current without a voltage, but you can have a voltage without a current.

You can try to think voltage as the electrical "force" with limitations, intent or the eagerness for the electrons to pass between the two points, and how quickly and far it can jump if granted the opportunity. The electrical forces that results in the eagerness for electrons to move effects not only electrons, but protons as well, but for most part they're heavy1 and are tied down to somewhat fixed objects while electrons can pass in between. The eagerness is a result of too many electrons in a location, or the lack of compared to for example the positively charged atoms.

That all being said, both sides doesn't have to end up in a 1:1 ratio of protons to electrons, there just has to be a difference of the ratio between protons and electrons between the two points.

For example if electrode A has 75 electrons and 80 protons while electrode B has 25 electrons and 160 protons, it'll still want to shoot over despite electrode A being deficient on electrons so that both sides will have an equal charge ratio of protons to electrons.1 33 electrons to 80 protons on electrode A and 66 electrons to 160 protons on electrode B.

You can think of country migration as another example, let's assume nobody flies for leasure and people will only want to permanently move to less densely populated areas - There are too many people in china as it holds like a third of earth's population, so there tends to be an outflow of people, with a very low rate of people entering china although that's largely due to political reasons which we shouldn't get into here because people see more land to use in places like Australia as it is the same-ish size as china with barely any people in it in comparison. which is also why Australia's oriental baby birth rates recently exceeded those of western descendants.

Anyway, once the electricity jumps, it may not want to jump again until enough voltage, or "pressure" has accumulated. In this case, static electricity passage from clouds or a static generation machine are good examples. They like to zap in intervals, and not continuous as it releases the energy, but doesn't have enough energy to sustain the zappy chain until the electrons pile up enough again to push some of it across to the other point.

The minimum voltage required for an electrical current to flow depends on the mediums (the shit that the electricity has to go through between the two points), and in the case of static electricity generator demonstration machine thing the main inhibitor medium is air. Air molecules inhibits the passage of electrons, but may take on a slight charge along with the electrode near them. Air requires very little voltage at small distances to get a zap to start, and because it is a small distance it's much easier to sustain a consistant current. However if you space them 10 metres apart, you need a hefty number of zeroes on the potential difference number to start a zap, and you'll need a lot more ontop of that to actually sustain a link.

With the migration example, we can say that the medium is the ocean, and the transporters can't make money unless they transfer a certain number of people over the water at once, and thus won't want to fly as frequently. The shorter the distance, the less it matters because you can fly regular flights with smaller aircraft, but the longer the distance, the more it matters because jets are more economically efficient with their seats sold and there aren't small aircraft capable of flying those large distances, not to mention less people willing to buy more expensive tickets to fly such long distances. Eventually with enough people flying the airline, you can get a steady stream of daily flights with multiple aircraft flying the route daily, but that requires a drastic increase in migrants.

Height Potential Energy

Note that the word I used here is "Height." The reason why I use "height" is to remove confusion with other types of potential energy which I may add to this page. For this case I'll use planet earth's gravitational acceleration.

Height potential energy is the height difference between two possible states.

Height potential energy in an aircraft or roller coaster car or even just a car rolling down a hill can be converted to a speed gain. Because Earth's acceleration is approximately 9.8 (m/s)/s, we can straight up see by the units that it means that we will accelerate to 9.8 m/s withing a second from standstill state in an ideal zero drag environment. Even though energy involves mass, because we're converting kinetics, we actually don't need to know the mass of an object to convert from height difference to speed difference. However, calculating how much height is lost within that one second isn't so easy. Because you're likely here from a flight sim and I trust you aren't a moron, I hope you will at least understand what I'm talking about here so I'll skip on the explanation because you're probably here for the maths.

Luckily, some smart dudes in the past came up with some equations, though unfortunately I didn't study them. ironically I passed my year 8 physics test with like 95% correct without memorising any equations whatsoever without knowing how to rearrange equations because I'm so shit at written maths but now we have the internet to help us.

Basic potential energy to speed conversion all relies on that one acceleration constant number of 9.8 (m/s)/s. Because the unit we see is (meters per second) per second, we know that over time will be squared so we will be getting a parabola, which is that fancy curve you get from getting a number multiplied by itself. However since the time is taken to accelerate the falling object to 9.8 m/s from zero within a second averages numbers 0 and 9.8 together by one second, we know that the distance fallen in that second is actually half of 9.8, therefore we can literally get a constant of half the acceleration multiplied by time squared for our distance.

Based off this, we can calculate that the distance covered in a second is actually simply 0.5 * 9.8 * time ^2 or if you want to be fancy,

Δs = (aΔt2)/2 

where Δ (delta) simply means change of,

s is displacement, basically distance coverered. Science probably assigned "d" to something they deemed more important.

a is the constant acceleration, and

t is time.

In the world of physics, such basic equations are grouped under something called kinematics.

Additionally, because we will be accelerating every second by the acceleration value, we can see that our velocity "v" gain will be also

Δv = (aΔt2)

However, distance loss and velocity over time isn't exactly helpful for aviators which you most likely are, but instead we will need the velocity to height relationship. Instead what we will need are to convert to velocity from a height state, not a time state.

Because gravity is constantly accelerating the object to the ground and we're concerned about distance and not time, we will need to flip that square to a square root relative to the ground, err distance (s), so we need to also multiply the external modifier (which was 0.5 before the flip) which are now internal by 2 and we will get another simple equation dictating our velocity equivalent "ve"for the given height displacement "s":2

ve = √(2aΔs)

If we have an example, I'm flying about mach 1, specifically 600 knots (~1111 kph, 309 m/s) true airspeed with zero wind in WT at 2000m below an enemy, that enemy above me will need to be at least around (309m/s - [√(2 x 9,8 x 2000) = 198 m/s]) which is around 110 m/s, or 213 knots to be able to jump me in a zero-thrust zero-drag flying condition and not fall behind.

Knowing your energy conversion ratio by feel is usually good enough, and is critical when you're for example lower than the opponent. It's usually a waiting game to get enough energy to intercept or have a decent chance in a dogfight without the enemy getting out of reach too quickly. However if you know you only have once chance as you're too slow to wait, you also need to time your lead based on how slow you will get when you get within guns or missile range - You wouldn't want to be too slow as it would make your aircraft unstable.

Anyway here are the graphs, I used a simple graphing tool which didn't allow me to scale the axis so I had to scale the units, be wary that you may need to multiply an axis by 10.

ALTITUDE vs SPEED graphs

m vs m/s (Also sorry the "divide by 33 to get feet" should be "divide by 0.33 to get feet" - my bad!)

m vs knots

m vs kph

feet vs knots

feet vs mph

Notes

1. With a massive difference between the protons and electrons, you will actually start to push into the boundries of chemistry and quantum science and how atoms bond together.

2. In hindsight, instead of going through that weird rearranging kinematic process from the gravitational acceleration constant alone (a = 9.8 (m/s)/s ) I could've just googled PE vs KE which gives you momentum energy (0.5mv2) and PE (mas, or mgh where g = accel and height). But the weird thing is, nobody teaches you that you can get the PE/KE conversion from just the value of gravitational acceleration alone, they need to teach that more often but I guess Einstein level maths bullshit is too much for the general human.