The E-Nerd series is back with a new blogpost! This series really amazes my inner child, always looking for weird innovations ready to create new entertaining markets! Even though many technologies already presented are impossible to be realised, such as The Matrix’s thermodynamic human power generator or Star Trek’s traction ray, a few others born from the genius of authors and fiction-addicted geeks have become reality, such as the hoverboard from back to the future, the lightsaber from Star Wars and many more.
The last invention is the flying car recreated by Psyonix in the quite famous video game Rocket League, where two teams of three cars battle in a football match-style competition. This kind of competition already exists in real life, with cars playing on football pitches and using real football goal post. In Rocket League, the developers went much further, as they added a rocket engine and explosives to permit the cars to jump and to skyrocket! Does it sound too wild to be real?
Rocket league: the basic physics assumptions
A videogame is created in the first place to offer a gameplay that is not boring or too complicated; therefore many aspects of reality are ignored. First of all, cars do not get damaged either from bumps against other cars nor when they hit the wall or the floor at speeds higher than 80km/h. It is instead possible for the car to explode when hit by another car travelling faster than the speed of sound .
Side note: the speed of sound is 79 km/h in the game, suggesting a low density air fluid.
The gravity force is here set to be 6.5m/s^2, which is 1/3 lower than the Earth’s. The rocket acceleration is instead 14.2m/s^2 and it will be considered constant to ease the analysis. The propeller is limited in the game to 100 units (more info on the unit conversion later in the article) while jumps are achieved through small explosions that are not limited. Moreover, there is no air resistance in the game and every object falls the same way. The car weight is uniform so that the physics of the cars are equal. The body shape is the only difference, but it is an important factor only for the gameplay.
The car can jump up to 1.5 meters while a second jump can be achieved through a second explosion, this time with a controlled direction. The outcome is very similar to a real car explosion when it has a balanced weight (no engine in it).
Rocket League: The car
To realise a car like this it is mandatory to first talk about its size. Through approximated values, cars are 1:4 models of real cars, therefore the average size is 120x80x30 cm.
The cars of this size used in competition weigh around 700 kg and use a common petrol engine. Considering a reduction factor of 64 in volume, we can also consider the weight to be 1/64th for a total weight of 11kg. Since the engine has to be substituted with a functional Jet Engine, I found that the “JetCat 220N” models for aeromodelling weighs 2 kg. Now in order to achieve 14.2m/s^2, it is necessary to have a load of 15.5 kg, which is easily obtained considering materials that are more resistant to high temperatures and impacts and weights that are necessary to rotate the car mid-air.
The ball is said to have a weight equal to 1/10 compared to the car, so it is around 1.5kg. This weight ratio is important for the gameplay as it determines the speed of the ball after an impact with a car. The impact is inelastic and the maximum speed achievable by the ball is 216 km/h, which is more like a set hard cap from the developers than a real physical value. The limitation is also due to the fact that the car keeps most of is momentum after the hit and to get the ball to go faster than 100 km/h it is usually possible only through a pinch with another car or the wall, such that the ball compression and its following expansion contribute to accelerate the ball.
The maximum speed
The cars’ maximum speed is 83 km/h, while 79 km/h is enough to reach the speed of sound. Given a lower gravitational force, the atmosphere is lower and therefore the air density is much lower, which is one of the main factors in the determination of the speed of sound.
The football pitch
The dimensions of the field are 102.4x82.4 meters, which is very similar to a real football field with 20 meters more on the sides. These additional meters are used here to create a curved fitting with the lateral walls that close the pitch. The walls are then closed on top with a closed ceiling that permits the best players also to create astonishing shots, where they drive on its first part, lose contact due to gravity and shoot in the falling. The ceiling is 20 meters high.
A classic match is 5 minutes long and the propeller is recharged more or less every ten seconds. The way this collection works is not known yet and it is possible to suggest a magnetic attraction to grab tanks of fuel. A full match may consume up to 3000 units of propeller fluid and it is possible to charge either 12 or 100 units of boost at one time. And how much energy can be obtained by a single unit?
The game gives different hints on the topic. For example it is possible to reach the ceiling with no final speed with 40 units of boost, while 70 units are consumed to reach the top in the lowest time possible equal to 2.3 seconds. The entire 100 units are instead used in 3.3 seconds, therefore the boost will be used for a third of the match.
The potential energy gain for a car of 15.5kg that reaches the ceiling is in the game equal to 2015 J. Since to reach the ceiling with no speed it takes 40 boost units and a common rocket engine has 40% efficiency, a single unit of boost corresponds to 125.9 J, with an average consumption of 151.1 kJ per game per car. This consumption corresponds to 105 Wh. Due to these values, it is possible to estimate a constant power of 3.8 kW while boosting. The basic fuel engine permits instead to reach a maximum speed of 50 km/h with a power that is near 2-2.5 kW.
Jumps! Here comes the magic! And they are the magic trick of the game as the car couldn’t fly otherwise! Even though the car can use a jet engine, the absence of air drag means at the same time an absence of air lift, which is the necessary force enabling airplanes to take off and fly. Therefore how can these cars move in three dimensions? They can jump and rotate on themselves. Once they get a nice direction the jet does its work and the car can move in any direction.
In order to rotate the car, it is necessary to have some moving masses inside the car, whose movement is counterbalanced by the car itself to conserve the momentum: similar to many people moving to one side of a boat. In this case it would be necessary to have an electrical component to force these movements against gravity when it is required.
Instead, jumps are recreated through small explosions starting from the centre of the car, as the explosion’s flames move equally in the different directions. A single jump permits the car to reach a height of 1.5m and immediately after it can explode a second charge to go even higher. The amount of energy required for a car of 15.5kg to reach that height is 151 J in the game. Therefore a small charge would probably be enough, but since the game permits an unlimited number of jumps it would be necessary to have an unlimited amount of explosives on board since the start of the match - that is unthinkable for a real application.
Moreover, the game permits a second jump in a certain direction and it permits dodging in one of the eight main directions. This would use the same principle as the first jump, but this time the direction can be chosen by the driver. This last jump can be done through the use of explosive charges positioned on a certain side of the car.
A second possibility is instead achievable through the use of compressed air or with the use of 2 charges of boost, this time directed towards the lower part of the car. Since such an engine would not stop us from using it for a single jump, but mostly use it for the entire game, it seems unthinkable to be the real case scenario. A secondary idea is that part of the air is compressed while the car moves and then it is released to recreate a movement. This principle results in the same as that of explosions but the expansion of the compressed air is much less effective. An explosion usually recreates a volume ratio of three orders of magnitude higher, while for a gas with the perfect gas approximation the ratio in pressure is equal to the ratio in volume required. Therefore, for a jump of 1.5m the car needs in its initial point a kinetic energy of 151J, which is equal to an instantaneous initial speed of 4.41m/s.
How could this kind of a rocket boost look in real life and how can jumps be recreated in real life?
A real life realisation:
The following part would not only check for feasibility of the idea, but it will also create a first hand estimation on the price.
The car itself can cost up to 700€ due to its quite large dimensions.
The propeller and the rocket engine
Let’s now consider the possibility to recreate this in real life. As previously stated, the acceleration is never constant, therefore before a prototype can be realised based on the previous data it requires more engineering studies. For now, it would be already good enough to consider some of that data to try to recreate a real model.
The jet engine that could be suitable for the game was a JetCat 220N, but on Earth the gravity force is 9.8 m/s^2 and its thrust would permit only an acceleration of 4.4m/s going upward. In order to maintain the same thrust with Earth’s gravitational force, 270N of thrust are necessary, suggesting a power around 5kW and speeds higher than 100km/h. Since a 270N engine does not exist, the “JetCat 300P” with a design thrust of 300N is chosen. The weight is increased by 0.5kg so the total weight of the car would be 16kg. This would permit the car to have an acceleration of 18.75m/s^2.
The fuel considered is kerosene and its consumption for the jet engine is 16.33 mL/s (we assume the weight does not change along with the fuel consumption to simplify). The consumption in the game is supposed to happen for a third of a five minute game, which means 100 seconds and a 1.63L of fuel. This amount of kerosene, although quite low, it is enough to blow up the car on a very strong impact.
The price for such an engine is around 2700€ that adds up to the 700€ of the car for a partial cost of 3400€.
The most important difference to be kept in mind is the starting time. Whereas in the game the engine works instantaneously, the real jet engine takes time to start and this would make it ineffective. A possibility would be to recreate the same jet engine to work with an electrically recreated reaction in order to make it more immediate, but the feasibility of such an engine is outside my knowledge (and if the reader has some suggestion, I would love to hear more)!
In order to recreate jumps there are two possible solutions:
- To create a small explosion;
- To use compressed air.
In order to have a model that is more similar to the game car a supercapacitor charged by an alternator in the wheels is used to detonate the explosive or to release the compressed air. The overall cost of the device is relatively low and won’t be considered in the analysis.
Let’s consider the explosion possibility, which may be more appealing for the simple implementation. A common explosive reaction can be achieved with NaN3, which is found in airbags. The compound reacts with the energy produced by the car crash and generates metallic Sodium (Na) and gaseous Nitrogen (N) which immediately expands the air bag. A reaction of 130g can produce up to 67 litres of Nitrogen, which would be enough to make a 70cm high cushion under the car. This is probably too much, but 100g would be more than enough. However, considering a general game, jumps are continuous and they can easily be done more than 100 times per game. That means that each car should start with more or less 10 kilograms more weight, which is unacceptable. A possibility is to consider the collection of new charges when a car reaches a charging point for boost, lowering this amount to few hundred grams of substance. The only possibility to consider this solution for a realistic project would be to change a little bit the game itself to make it realistic and to develop a similar system like it happens in the game for the propeller.
Another reason why this is unlikely to happen is the cost of the NaN3, which is around 1000€/kg and a single match would require 10 kg of explosive per car, which makes the cost for a single game higher than 60000€ for a 3v3 match.
And the car can as well explode!
This happens at least once per game, so cars have to be rebuilt again after the games, although a second or a third vehicle is always ready to substitute the other one in order to seek revenge! This would add the need to have an extra 3400€ more per car accounted. The same explosion, but less effective could be obtained with more common and less expensive reactions although their effect is lower and require more mass to obtain the same result.
Furthermore, the use of explosives to recreate jumps increases the stress for the materials. Although this is partially shared with the need to sustain up to 750°C given by the jet-engine, it would increase the materials cost substantially. Therefore this solution is discarded.
The second idea is instead to use compressed air. It is either possible to consider a compressor working when it is necessary (like a jet-engine it would create thrust for a jump) or a compressor that stores air at a much higher pressure to release it like an explosion in a second moment. This second idea seems to be more realistic and feasible and it would also avoid any temperature issue given by explosions. On the other side, the expansion of the gas is proportional to the volume ratio. Without temperature differences, it is possible to reach a pressure ratio of 200, while a more realistic ratio would be 100. That means that a jump of 1,50m would be achievable with the emission of air that pushes the car up at a speed of 4.41m/s. To do so it is supposed to release at least enough air to fulfill 20 cm in height, which equals to 0.2 m^3 of air released in a short time. Looking at the game performances, the release lasts more or less a tenth of a second. The compressor volumetric flow required is 2 m^3/s for a mass flow of 2.58 kg/s.The power released can roughly be assumed to be the same as required for the in-game values, therefore 151J released in 0.1s, for a 1.5kW volumetric compression and expansion. For real life considerations, the additional presence of 0.5kg introduces some variation to the car’s physics although they are very small. Moreover, the compressor works only while the car touches all four wheels on the ground, to avoid any unbalance of the car.
It appears feasible to create a real life model, although it is engineeristically challenging. Are you willing to get your hands dirty and make a prototype to get the real competition starting?
Let me know your ideas and feelings! I’ll be happy to hear back from you.
By Jacopo Sala
The CommUnity Post
A great thanks to the Rocket Legue Reddit community for part of the information about the field and to the Rocket Science YouTube Channel for the insights! He is even crazier than this article, give it a check!