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Off-topic part: Since I have no better place to do that, I just want to apologize to all the people that are waiting for me to respond to things. Especially to LordAizenSama given that I wanted to create that one thread we talked about 12 days ago. September was a very stressful month for me and I was a bit tired out after it and had some things to catch up on, so I wasn't very active lately.ÔÇ¿ÔÇ¿
With that to the more interesting on-topic part:
When it came to explosion speed we have a established method to calculate the speed of a character if we can compare his movement to the distance the explosion expanded in that time. Since the speed of the shockwave, used for that method, quickly declines after the explosion we to this point lacked a good method to calculate how fast a character has to be in order to outrun an explosion.ÔÇ¿
In order to solve this I have written a simple calculator. Uncharacteristically for me it is not based on analytic methods.
How it works
The principle it works on is as follows:
Beginning at one meter per second it checks whether the given speed is sufficient to escape the explosion. If it is outputs that speed, if not it checks whether 1 meter per second more works.
The method checking whether the speed is sufficient to escape or not works as follows:
Using the equations taken from the source-code of this calculator, it is calculated how long it would take for the explosion to expand 0.1m. Then it is calculated how far away a character starting at the specified distance, with given movement direction and the speed to be checked has moved from the origin of the explosion. If the character is closer to the origin of the explosion than the shockwave, the shockwave must have past the character by, so it must have been hit. In that case the method responds that the speed is insufficient. If the character on the other hand is further away of the origin, than the shockwave the process is repeated with the shockwave having expanded 0.1 m further.ÔÇ¿
This continues either until the character is hit by the shockwave or until the shockwave has expanded to the maximum extension for which the formulas give correct results. In the latter case the method responds that the character escaped.
how to use (explanation on input and output values)
So at the right you see the interface of the calculator. It has 4 values that have to be input and 3 values that are output.
The Start Distance is the distance the character has to the origin of the explosion at the point in time the explosion happens in. The value has to be input in meter.
The Charge Weight is the weight of the explosive. The Explosion Speed Calculations page describes on how one can approximate that value. The value has to be input in kilogram.
The "Degree of Derivation from Expansion Direction" is an angle, input in radians. This angle is there in order to describe in which direction the character dodged. If you imagine a line between the point the character starts at and the origin of the explosion, then 0 would mean that the character runs further into the direction of that line away from the origin of the explosion. If the character takes another path, then the Degree of Derivation is the angle between the 0 path and the path the character actually takes. So running straight towards the explosion is ¤Ç .
The Explosive Type is the type of Explosive used. This can be figured out in the same way that is described on the Explosion Speed Calculations page.
The "Speed to outrun Explosion" value is the speed in m/s necessary to escape the shockwave of the explosion.
The "Time of arrival at Start Distance" is the time it takes the Shockwave to reach the Start Distance that was input. This way this calculator can also fulfil the task that is already done by the UN calculator, as specified on the Explosion Speed Calculations page. The unit is given in ms.
The "Closest to Shockfront at" value is a control value (see the following section). It specifies at which distance from the origin of the explosion the shockwave catches up closest to the character when it travels with the "Speed to outrun Explosion". It is given in meters.
Known flaws: Things one has to keep in mind when usingÔÇ¿
I will use a case from To Aru Majutsu no Index as example: "The response had come from quite close nearby. Mugino had been hit by a counterattack with a handgun the previous time, so she quickly and forcefully twisted her body around and fired Meltdowner without checking on her target. A brilliant beam of light shot out and the fighter jet in its path melted orange. But just before it did, Mugino saw what was there. A service tractor and a long narrow bomb packed in what looked like a large pipe were in the place she had fired on. On top of those was a wireless headset that was set at its highest volume so the sound would escape into the surrounding area and a fiberscope with a wireless LAN that would be used for aircraft maintenance. She didn't have time to think about it. Before she could think a single thought, the 200 kg bomb that she herself had struck with intense heat split open and created a large explosion that enveloped the other bombs, the missiles, and the airplane fuel. Hamazura was hiding at a distance, but he did not escape unharmed. He had found an electric tractor-like vehicle used for moving the fighters and had been silently travelling at high speed away. He had hidden behind cover about 500 meters from the explosion."
[...]
""Did you reallllly think this kind of mass produced weaponry could take out the #4, Hamazuraaa?"
"****! ****, ****, ****!!" Hamazura desperately tried to suppress the intense pain eating into his ear, gripped his handgun with both hands, and fired. But Mugino suddenly disappeared. She had fired Meltdowner like a rocket engine. She must have escaped the 200 kg bomb the same way. With the sound of a blunt weapon being swung, Mugino moved outside of his vision."
So the bomb in question was 200 kg. As usually I will guess on it being TNT. Since it was stated to be quite nearby I will estimate the distance between Mugino and the bomb to be 2 meters. For the Degree of Derivation I will choose 0, since that should give the lowest result.
Putting everything into the calculator I get 1458.0 m/s as result or Mach 4.24330617. High end Supersonic+.
TODO
I can partly solve the last problem quite easily by making it so that a range until which to check can be specified. That I will probably do sometime soon.
Help wanted
If someone wants to look over my sourcecode and do some testing to see if everything works correctly before I put this on some official page, I would encourage that. So on request I can give out the sourcecode. In general I am also open for suggestions on improvement (I don't make promises on improvement though).
Download
Here is a download link for the current version (hope mediafire is ok for everyone).
With that to the more interesting on-topic part:
When it came to explosion speed we have a established method to calculate the speed of a character if we can compare his movement to the distance the explosion expanded in that time. Since the speed of the shockwave, used for that method, quickly declines after the explosion we to this point lacked a good method to calculate how fast a character has to be in order to outrun an explosion.ÔÇ¿
In order to solve this I have written a simple calculator. Uncharacteristically for me it is not based on analytic methods.
How it works
The principle it works on is as follows:
Beginning at one meter per second it checks whether the given speed is sufficient to escape the explosion. If it is outputs that speed, if not it checks whether 1 meter per second more works.
The method checking whether the speed is sufficient to escape or not works as follows:
Using the equations taken from the source-code of this calculator, it is calculated how long it would take for the explosion to expand 0.1m. Then it is calculated how far away a character starting at the specified distance, with given movement direction and the speed to be checked has moved from the origin of the explosion. If the character is closer to the origin of the explosion than the shockwave, the shockwave must have past the character by, so it must have been hit. In that case the method responds that the speed is insufficient. If the character on the other hand is further away of the origin, than the shockwave the process is repeated with the shockwave having expanded 0.1 m further.ÔÇ¿
This continues either until the character is hit by the shockwave or until the shockwave has expanded to the maximum extension for which the formulas give correct results. In the latter case the method responds that the character escaped.
how to use (explanation on input and output values)
So at the right you see the interface of the calculator. It has 4 values that have to be input and 3 values that are output.
The Start Distance is the distance the character has to the origin of the explosion at the point in time the explosion happens in. The value has to be input in meter.
The Charge Weight is the weight of the explosive. The Explosion Speed Calculations page describes on how one can approximate that value. The value has to be input in kilogram.
The "Degree of Derivation from Expansion Direction" is an angle, input in radians. This angle is there in order to describe in which direction the character dodged. If you imagine a line between the point the character starts at and the origin of the explosion, then 0 would mean that the character runs further into the direction of that line away from the origin of the explosion. If the character takes another path, then the Degree of Derivation is the angle between the 0 path and the path the character actually takes. So running straight towards the explosion is ¤Ç .
The Explosive Type is the type of Explosive used. This can be figured out in the same way that is described on the Explosion Speed Calculations page.
The "Speed to outrun Explosion" value is the speed in m/s necessary to escape the shockwave of the explosion.
The "Time of arrival at Start Distance" is the time it takes the Shockwave to reach the Start Distance that was input. This way this calculator can also fulfil the task that is already done by the UN calculator, as specified on the Explosion Speed Calculations page. The unit is given in ms.
The "Closest to Shockfront at" value is a control value (see the following section). It specifies at which distance from the origin of the explosion the shockwave catches up closest to the character when it travels with the "Speed to outrun Explosion". It is given in meters.
Known flaws: Things one has to keep in mind when usingÔÇ¿
- The pi error: When the Degree of Derivation gets closer to pi the speed to outrun the explosion the program gives becomes more inaccurate. To be specific it becomes smaller than it should be. The Reason for that can be easily seen if on looks at the case of the Degree of Derviation being chosen as pi. In this case the character would in the scenario run towards the origin of the explosion. It should be absolutely impossible to outrun the explosion this way, so we would expect the program to result in an error or give infinite as speed necessary to outrun the explosion. In practice you will only get a very high value though. I believe that is due to the fact that the programm only checks wether the shockwave is further away from the origin than the character at 0.1m intervals. Essentially the speed vaue one get in the result here, will be the one high enough so that in one check the character is still in front of the shockwave and at the next check the character has moved all the way to the other side of the of the explosion and shockwave. In reality that woud mean that the character ran through the explosion and got hit, but since the program doesn't check the characters position during that movement (if the speed if high enough) it doesn't notice that.ÔÇ¿
- Not outrunning the explosio: Take note that the character is said to have outrun the explosion if it left the range from the explosion origin in which the shockwave can be correctly approximated. That means for very large Start Distance the character might has to only move a very short distance compared to the shockwave. If the value to outrun the explosion becomes lower than the speed of sound, this is likely the reason.ÔÇ¿
- What if a character is cought in the shockwave or the shockwave is stopped at some point?: In that case as well as whe only the fireball was escaped from the "Closest to Shockfront at" value becomes important. As long as that value is smaller than the distance to the origin when the character was cought in the shockwave, when the shockwave was stopped or that of the fireball (depending on which case we are considering) the estimation is still correct.ÔÇ¿
I will use a case from To Aru Majutsu no Index as example: "The response had come from quite close nearby. Mugino had been hit by a counterattack with a handgun the previous time, so she quickly and forcefully twisted her body around and fired Meltdowner without checking on her target. A brilliant beam of light shot out and the fighter jet in its path melted orange. But just before it did, Mugino saw what was there. A service tractor and a long narrow bomb packed in what looked like a large pipe were in the place she had fired on. On top of those was a wireless headset that was set at its highest volume so the sound would escape into the surrounding area and a fiberscope with a wireless LAN that would be used for aircraft maintenance. She didn't have time to think about it. Before she could think a single thought, the 200 kg bomb that she herself had struck with intense heat split open and created a large explosion that enveloped the other bombs, the missiles, and the airplane fuel. Hamazura was hiding at a distance, but he did not escape unharmed. He had found an electric tractor-like vehicle used for moving the fighters and had been silently travelling at high speed away. He had hidden behind cover about 500 meters from the explosion."
[...]
""Did you reallllly think this kind of mass produced weaponry could take out the #4, Hamazuraaa?"
"****! ****, ****, ****!!" Hamazura desperately tried to suppress the intense pain eating into his ear, gripped his handgun with both hands, and fired. But Mugino suddenly disappeared. She had fired Meltdowner like a rocket engine. She must have escaped the 200 kg bomb the same way. With the sound of a blunt weapon being swung, Mugino moved outside of his vision."
So the bomb in question was 200 kg. As usually I will guess on it being TNT. Since it was stated to be quite nearby I will estimate the distance between Mugino and the bomb to be 2 meters. For the Degree of Derivation I will choose 0, since that should give the lowest result.
Putting everything into the calculator I get 1458.0 m/s as result or Mach 4.24330617. High end Supersonic+.
TODO
I can partly solve the last problem quite easily by making it so that a range until which to check can be specified. That I will probably do sometime soon.
Help wanted
If someone wants to look over my sourcecode and do some testing to see if everything works correctly before I put this on some official page, I would encourage that. So on request I can give out the sourcecode. In general I am also open for suggestions on improvement (I don't make promises on improvement though).
Download
Here is a download link for the current version (hope mediafire is ok for everyone).
