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Halo 2 Projectile Motion Research Project - 03-24-2011 , 11:40 PM


You guys didn't seem as interested in my last thread. I don't blame you. I didn't leave much information on how I figured everything out. Well go I'll go into detail how I did it right here. It's probably in the wrong forum but this is the most active of the Halo 2 forums so I'm posting it here. I won't go into how I modded it but just talk about the experiments I did.

Introduction

The reason I did this research was because I wanted to develop a way to complete any launch using a warthog. It's not as painstakingly hard as doing it without mods but I wanted to take a more controlled approach to warthog launching that uses math and logic. The only way to do this is to use mods.

For warthog launching there are two parameters you want to control, the warthog's initial speed, and the direction of that initial speed. With that and the coordinates of the beginning and ending positions of the launch you can describe the entire path of a projectile. The challenge in using this method is finding how to relate the initial conditions to the setup of the launch. What I hypothesized is that the only thing that affects the initial speed is the force on the grenades and the only thing that affects the direction is the position of the grenade.



Here I have a picture that shows the position of the grenade. It is always placed along the Y axis center of mass(this ensures that it launches in a straight line) and placed distance d away from the X axis center of mass. By changing this distance I am able to adjust the angle of launch.

Experimental Setup

With any experiments measurements need to be made and I make three types of measurements:time, length, and angle.

The time measurement is easy. I use two methods for measuring time. The first one is simply using a stop watch and the other is filming and looking at the video to determine the time. For the second method I loaded the clip into a video editing program and found the exact time an certain event started and the exact time that same event ended and subtracted the two times.

The length and angle measurements are trickier to find. Both measurements required me to mod a map. As for the the length measurements I put these markers every 10 length units and i numbered every 5 of the markers. From these markers I can determine how far I have launched. Measuring angle required me to set up angled markers at every 10 degrees so I can measure the initial angle of the launch.

I have two experimental setups:one is for measuring the height of a straight up launch and another is for measuring the angle and distance of an angled launch. Unfortunately I don't have the first experimental setup but I do have a video of the second experimental setup.

http://www.youtube.com/watch?v=YilrW1g3Hro

The straight up launch setup consisted of a platform from which I launched from which had a bullseye bitmap on it. Then every 10 length units above the platform there are plates with no collision model and are used for measuring the height. These plates have numbers to mark the distance similar to the other setup. I also have it setup so that the warthog and a plasma grenade, used to launch the warthog, are spawned at fixed regular time intervals and that the grenade spawns a few seconds after the warthog.

Experiment #1

The whole purpose of the experiment is to find the acceleration due to gravity(g) of the game. This experiment involves dropping from a known height and finding out how long it takes to fall a certain distance. I used a bsp viewer to find the starting and ending Z coordinate of the of the fall and subtracting the two values will get you the total height. Then the time can be found using one of he methods mentioned in the introduction. With the two values g can be calculated by this equation

h is the height and t is the time.
Another method for finding g is using the straight up launch setup. Though in order to use this method you will need to know the warthog's center of mass which is found in the next experiment. With the first launch measure how high the warthog goes then the next time it launches measure how long it's in midair. Since you measuring both the time it takes to get to the peak of the launch as well as the time it takes to fall you will need to divide by the time by two, or just use this equation

This experiment should be done many times and then an average should be calculated between the obtained values.
I ended up with a value of 4.06 Hl/
s2.(Hl is my abbreviation for the halo length unit).

Experiment #2

The purpose of this experiment is to find the center of mass in the X and Y directions. Before I go into the experiment there is one thing I need to talk about. When you place a warthog at a certain coordinate on a map you are placing it at a point(placing point) on the warthog at that certain coordinate. This point is not the same as the center of mass. Let me refer you to the picture above for this next part. This placing point does lie on the Y axis center of mass but does not lie on the X axis center of mass.

This experiment determines this distance between the
X axis center of mass and the placing point. This is basically done by a guess and check method. To do this experiment you will need the straight up launch setup. This setup has a platform with a bullseye on it. Start by placing the launching grenade underneath the placing point and see which direction it launches. Make sure the grenade has a very high force. Then move the grenade along the Y axis center of mass in the direction the warthog launches. Repeat this step until the warthog launches from and lands directly on the center of the bullseye.

I found 0.17925 Hl to be distance between the placing point and the center of mass of the warthog. Now every time a straight up launch is done the grenade is placed right under the center of mass. Every time an angled launch is done the starting point of the launch is at the center of mass of the warthog, not the placing point.

Experiment #3

The purpose of this experiment is to find the relation between the force of a grenade and the initial velocity of the launch. This experiment uses the straight up launch setup. Basically the grenade stays in the same
place, under the warthog's center of mass, for all of the launches . The force of the grenade is what is variable. Launch the warthog at a force of about ten and measure how high of the warthog goes. Repeat this step increasing the force of the grenade. Once You gathered data for forces up to 140 you can calculate the initial velocity of the launches using this equation


Vi is the initial velocity, g is the acceleration of gravity and h is the height of the launch. Here is a table of values I got from the experiment



As you can see the initial velocity doesn't go much higher for very high forces. There is actually a critical force at 133 where the initial velocity doesn't go up very much from there.

Experiment #4


The purpose of this experiment is to determine the initial launch angle based on a distance d shown in the first picture of the post. Remember this distance represents the distance between the X axis center of mass and the placement of the grenade. Here I use the angled launch setup that is shown in the film earlier in this post. This experiment involves holding the force fixed and varying the this d value. I start the experiment with a d value of 0.1 Hl and I fix the force at 60.
I measure the angle of the launch, using the angled markers, as well as the distance of the launch. The pause feature of the yelo trainer comes in handy here. I repeat the experiment increasing d at regular increments. Here have a measured value of initial angle as a function of d. The initial angle can also be calculated using the distance of the launch as well as the height calculated in experiment #3 for the corresponding power. So since my power for all launches was 60 the height is 243. This equation is



x is distance and h0 is the corresponding height
Note that when using this equation any angles that are above 45 degrees need to be subtracted from 90.
Here is the data I collected for the experiments I did.


The #NUM! means that one of my measurements was slightly off, but I'm not too worried about it. I'm suprised and also glad how well my measured and calculated angles matched up. It show I was able visually figure out the initial angle of the launch without too much error.

So now that I've got data to be able to complete just about any launch out there. Though I don't know how reliable this data is for low angled launches I noticed that if the grenade explodes too far away from the warthog then the initial velocity is decreased and my original hypothesis would not be correct. Either way I've just gone into great detail how I figured out how to do a mathematically accurate warthog.

Application

Now that we have this information we can apply it to an actual launch. This launch I'm applying it to is from the bottom of Cairo Station to the highest point. In order to define this launch I need to find the starting and ending coordinates as well as the overshoot, which is how much higher the warthog launches beyond the ending point. For campaign launching you wouldn't want the overshoot to be above a certain value or else the fall timer will kill you.

The starting point for my launch is [-300,0,-733] and the ending point is [0,0,248.3]. I also chose an overshoot value of 10 Hl. Now it would be more convenient to change the coordinate system to a two dimensional system whose origin is at the starting point. Now the starting point is [0,0] and the ending point is [300,981.3]([x,y]). The first value is the horizontal distance and the second value is the vertical distance.

Now we can use these values to find the initial velocity and angle of launch.But first the initial velocities in both the x and y directions need to be calculated. These are the are the equations to find the components of the initial velocity.




x and y are the x and y distances from the starting point to ending point, p is the overshoot and g is the acceleration of gravity. Then you can use these equations to find the initial velocity and angle.



The angle here is shown as greek letter theta.
With these two values you can look at the tables of data I constructed in experiments 3 and 4 to find the corresponding force and grenade position values. You most likely wont be able find the exact initial velocity and angle values in the tables which is why you will need to use linear interpolation. Here is a wikipedia link on linear interpolation.

http://en.wikipedia.org/wiki/Linear_interpolation

Unfortunately when I found out the angle I needed for the cairo station launch it was higher than 80 degrees(about 83 degrees) so I took a guess at what the grenade position should be and I guessed 0.08 Hl. This got me very close to the top but wasn't accurate enough. I then changed it to 0.0825 and this value launched me right onto the highest point.
Here is the video to that Launch

http://www.youtube.com/watch?v=g716qIw36vE


I hope you guys enjoy reading this in depth look at the research I did on halo 2's projectile motion.

This whole thing was my attempt at practicing how to write research paper. I know it's not like a professional paper but I'm not worrying about that on HIH. I'm going have to write one for my senior project and I figured I can write a more laid back paper without worrying about too many mistakes or length or clarity but I hope you give me a heads up if something doesn't make sense. I'm tired and I'm not going proofread this tonight. I will edit this post tomorrow with how to apply this information to an actual launch and I will proofread then.

I know this would make a whole lot sense if I had videos but I lost my straight up launch modded map and I don't have time to remake it.

Last edited by Duelies; 04-01-2011 at 11:17 AM. .

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03-25-2011 , 01:27 AM


Fascinating, all of my launches and even my swordflys were calculated using ht, angle, length and speed/time but I only used them for proportions so I could take the info to another map or level and just change the angle and length and such.

I used the information in a swordflight so I could measure the flight distance to land exactly where I wanted. I would practice the angles I wanted by timing the controller movement so I could literally find the desired angle with eyes closed. I could not have done my swordfly to the OS Scarab gun from underwater without establishing the golden triangle (of sorts).

I did not get into it quite as much for the launches, though. The exact same setup after a CP would yield widely varying results, similar to bad gunpowder that burns at varying rates. But for your experiments taking an average would give you good info. eventually.

The Spectre is the vehicle I used most for finding angles and distance because of the pinpoint accuracy by using the nose as XY. Fun stuff and I used Spectre units, lol.

Some interesting things I learned about swordflying:
The rate of SF speed is constant unless you hit an object or touch a wall and that slowdown drastically changes the distance of the flight. So the distance you travel away from an enemy will = the time it takes to travel back the distance at the constant rate of a normal SF. The distance changes dramatically depending on how much your rate of speed has slowed and you will lose swordfly ability and drop when the time is up.

The angle change when you press A during a SF is 40 degrees +-. (That's what I recall but my memory is faulty)

Edit: Oh yeah, I forgot, for launching there was always the 10 times rule which threw everything off but that was the one I always wanted.

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03-25-2011 , 06:10 AM


I never really got into launching/tricking a lot in Halo 2 but that was a very interesting read. I wonder if any of your tests and the info gained could be applied to any other Halo game.

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03-25-2011 , 05:46 PM


Quote:
Originally Posted by Muzza View Post
I never really got into launching/tricking a lot in Halo 2 but that was a very interesting read. I wonder if any of your tests and the info gained could be applied to any other Halo game.
It is hard to apply this in reality, because there can be big differences considering the precondition on the same CP (as grumpy said). This means that random is going to kill it in the end, at least for launching. The main problem is the grenade power, which changes after every CP revert. Duelies always used the same power to work it out, but in reality you just don't have that condition.

However, this was a great read. I always dreamed of there being formulas for launching. Thanks for giving launching some more logic. This makes me feel like a b00n.

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03-26-2011 , 03:22 AM


well, this is too much >.>

It would be logical or something but seeing that formulas reminds me of my old school math classes (which sucked). Seeing a wall of text about physics and trying to understand it in english is too much for me

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03-26-2011 , 03:41 AM


Quote:
Originally Posted by xlax007 View Post
well, this is too much >.>

It would be logical or something but seeing that formulas reminds me of my old school math classes (which sucked). Seeing a wall of text about physics and trying to understand it in english is too much for me
I know, the reality was we drove out to a spot and launched a 1,000 times, then we could see all the angles afterward.

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03-26-2011 , 04:03 AM


@grumpy: did you double post just to get post number 7 or was that just an honest but convienient mistake

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03-26-2011 , 04:07 AM


Quote:
Originally Posted by LDG View Post
@grumpy: did you double post just to get post number 7 or was that just an honest but convienient mistake
I have no idea what you're talking about. I'm Mr. innocent, refresh and look again.

 

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