Forum: empire-en
Board: [589] Strategy & Tactics Discussion
Topic: [104557] Speed equation
[1733403]
Keenanxbox [None]
:: April 2, 2014, 11:39 a.m.
oooh so much math ooh my brain^^
[1733498]
Lord Porky [None]
:: April 2, 2014, 2:38 p.m.
dueltheabdul wrote: »Okay... I will check that out. Have you tested the last part (bolded) of the post? If you did, then we over-complicated everything.
Yes, Abdul - tested it over many distances, up to over 1100 spaces.
So a level 1 stables with the lowest option with 300 spaces would have a speed bonus of 400%?
No, that would be 13.3...% every 10 spaces, and a level 3 Stables only gives you 13%, there.
Cat said it's 6% (I believe this is for the 'Coins' option, level 1 Stables).
30 x 6% = 180%, so the speed over 300 spaces should be 2.8 times normal.
[1733753]
dueltheabdul (INT1) [None]
:: April 2, 2014, 9:52 p.m.
Lord Porky wrote: »Yes, Abdul - tested it over many distances, up to over 1100 spaces.
No, that would be 13.3...% every 10 spaces, and a level 3 Stables only gives you 13%, there.
Cat said it's 6% (I believe this is for the 'Coins' option, level 1 Stables).
30 x 6% = 180%, so the speed over 300 spaces should be 2.8 times normal.
Can you show how you calculated the times using actual numbers?
I tried to do what you described in your last post, but it didn't work for me.
I probably did something wrong, so can you show me?
Thanks Porky
[1733770]
cat402 [None]
:: April 2, 2014, 10:18 p.m.
Lord Pordky, that does not work. You will get a larger time speed for short distances. For example, 3.2. The uunit was 25. The travel time was aroudn 12 mintues and the calculation gave me 25.
3.2/10=.32*.6=.192+25=25.192, which is nowhere near 12. Can you explain it a bit more? I don't think we really understand what you mean.
3.2/10=.32*.6=.192+25=25.192, which is nowhere near 12. Can you explain it a bit more? I don't think we really understand what you mean.
[1733789]
Lord Porky [None]
:: April 2, 2014, 10:46 p.m.
Sure, Abdul. We'll figure out how much the Stables increase the speed, add that to the walking speed, then we have our "horse" speed. Then see how long it will take to go the distance.
1000 space trip, 'Coins' option with horses gives me 13% faster speed for every 10 spaces. (Level 3 Stables.)
1000/10 = 100 speed increases. 100 x 13% = 1300%, or an additional 13 times as fast as walking speed, so when that's added to the base walking speed, it will be 14 times as fast, overall.
Walking speed = 214.285 seconds per space. That's how long it takes for the walking troops to go one unit of distance. We want to be accurate here, as any error will get multiplied over the course of the trip, and in this case it's a long one. I got that 214.285 figure by putting in a 1000 space trip for the troops walking. (Just changed the coordinates along one axis by 1000 from one of my castles.)
Here, it is expressed as 'time per unit of distance.' We could also do it as 'spaces per second,' but there we get a repeating decimal: .00466666666... spaces per second.
214.285 seconds per space, now we are going 14 times as fast = so we divide the time by 14.
New speed = 15.306071 seconds per space. Multiply by 1000 for a 1000 space trip, and we have 15,306 seconds. 4:15:06 is what that works out to, and the travel planner in the game agrees, to the second.
________
Done with the 'spaces per second' figure:
.0046666 x 14 = .0653324 = our 'horse' speed.
Time = Distance/Speed.
Time = 1000/.0653324 = 15,306 seconds. Same result.
________
Shorter trip example:
47 spaces. 4.7 x 13% = 61.1% faster speed with the horse 'Coins' option. Total speed will thus be 161.1% of walking velocity, or "1.611 times as fast."
214.285 / 1.611 = 133.01365 seconds per space.
Multiply that by 47 spaces = 6251.6 seconds = 1 hour, 44 minutes, 11.6 seconds. Game says 1:44:11.
_______
Done with spaces per second:
.0046666 x 1.611 = .0075178 spaces per second on horseback.
47/.0075178 = 6251.8 seconds.
This was using a handheld calculator.
_____
Cat, lots of math and perhaps "too much" explanation, above, but all we are doing is finding the exact walking speed, and then calculating the 'horse' speed.
Example: if your Stables give 6% faster speed for every 10 spaces, then for a 20 space trip, the new speed would be 112% or 1.12 times as fast.
20/new speed = time.
(The "speed" number for units in the game means nothing, directly, as far as I can tell. We can say that a 75 speed unit is 3 times as fast as one with a 25, but we still need to start out figuring the actual rate of the walking speed, either spaces per second or seconds per space.)
1000 space trip, 'Coins' option with horses gives me 13% faster speed for every 10 spaces. (Level 3 Stables.)
1000/10 = 100 speed increases. 100 x 13% = 1300%, or an additional 13 times as fast as walking speed, so when that's added to the base walking speed, it will be 14 times as fast, overall.
Walking speed = 214.285 seconds per space. That's how long it takes for the walking troops to go one unit of distance. We want to be accurate here, as any error will get multiplied over the course of the trip, and in this case it's a long one. I got that 214.285 figure by putting in a 1000 space trip for the troops walking. (Just changed the coordinates along one axis by 1000 from one of my castles.)
Here, it is expressed as 'time per unit of distance.' We could also do it as 'spaces per second,' but there we get a repeating decimal: .00466666666... spaces per second.
214.285 seconds per space, now we are going 14 times as fast = so we divide the time by 14.
New speed = 15.306071 seconds per space. Multiply by 1000 for a 1000 space trip, and we have 15,306 seconds. 4:15:06 is what that works out to, and the travel planner in the game agrees, to the second.
________
Done with the 'spaces per second' figure:
.0046666 x 14 = .0653324 = our 'horse' speed.
Time = Distance/Speed.
Time = 1000/.0653324 = 15,306 seconds. Same result.
________
Shorter trip example:
47 spaces. 4.7 x 13% = 61.1% faster speed with the horse 'Coins' option. Total speed will thus be 161.1% of walking velocity, or "1.611 times as fast."
214.285 / 1.611 = 133.01365 seconds per space.
Multiply that by 47 spaces = 6251.6 seconds = 1 hour, 44 minutes, 11.6 seconds. Game says 1:44:11.
_______
Done with spaces per second:
.0046666 x 1.611 = .0075178 spaces per second on horseback.
47/.0075178 = 6251.8 seconds.
This was using a handheld calculator.
_____
Can you explain it a bit more? I don't think we really understand what you mean.
Cat, lots of math and perhaps "too much" explanation, above, but all we are doing is finding the exact walking speed, and then calculating the 'horse' speed.
Example: if your Stables give 6% faster speed for every 10 spaces, then for a 20 space trip, the new speed would be 112% or 1.12 times as fast.
20/new speed = time.
(The "speed" number for units in the game means nothing, directly, as far as I can tell. We can say that a 75 speed unit is 3 times as fast as one with a 25, but we still need to start out figuring the actual rate of the walking speed, either spaces per second or seconds per space.)
[1733826]
cat402 [None]
:: April 2, 2014, 11:45 p.m.
As far as I know, and I have tested it, the pseed unit is how far the unit can walk in 100 minutes. I will look at this more tomarrow when my brain wakes up agian.
[1733846]
cat402 [None]
:: April 3, 2014, 12:30 a.m.
I jsut found a very accurate speed eauation. It is
t=(100/s)d
This gets you the time in minutes.
Graph:Attachment not found.
The small dispacement with some points is my inaccurate graphing.
Red=equation.
Blue points are data.
y is time in minutes
x is unit speed.
If this works for eveyrone else I;ll update the first post with this.
t=(100/s)d
This gets you the time in minutes.
Graph:Attachment not found.
The small dispacement with some points is my inaccurate graphing.
Red=equation.
Blue points are data.
y is time in minutes
x is unit speed.
If this works for eveyrone else I;ll update the first post with this.
[1733861]
dueltheabdul (INT1) [None]
:: April 3, 2014, 12:51 a.m.
I jsut found a very accurate speed eauation. It is
t=(100/s)d
This gets you the time in minutes.
Graph:Attachment not found.
The small dispacement with some points is my inaccurate graphing.
Red=equation.
Blue points are data.
y is time in minutes
x is unit speed.
If this works for eveyrone else I;ll update the first post with this.
Yeah that actually works pretty well.
[1733893]
Lord Porky [None]
:: April 3, 2014, 2:44 a.m.
As far as I know, and I have tested it, the pseed unit is how far the unit can walk in 100 minutes. I will look at this more tomarrow when my brain wakes up agian.
The problem with that in-game number is that any modifications - and there are many: Commander bonus, Research, wartime, other alliance bonuses, etc. - will change the unit speed.
To have any sort of usable accuracy, the walking or horse-riding speed must be determined. Then, if the distance is known, the travel time can be too.
[1733902]
dueltheabdul (INT1) [None]
:: April 3, 2014, 3:05 a.m.
Lord Porky wrote: »The problem with that in-game number is that any modifications - and there are many: Commander bonus, Research, wartime, other alliance bonuses, etc. - will change the unit speed.
To have any sort of usable accuracy, the walking or horse-riding speed must be determined. Then, if the distance is known, the travel time can be too.
The unit speed can be determined then plugged in.
We would have 2 separate formulas. One for travel time and one for Speed with bonuses.
I would guess that the speed with bonuses formula would look similar to this:
S= (D/10) *(H+ B/100)+1 * s
S = speed with Bonus
D= distance
H= Horse Bonus
B= speed bonus from commander
s= original speed of unit.
This is only theoretical. Give me a bit to test it out.
_________________
Edit: Okay so Porky your method works fine as expected. But the commander percentages do not follow the same method.
Usually you would do for example 300 spaces divided by 10. And then multiply it by 6 (level 1 stables coins). If you have a commander bonus, you would do 30*(6+C/100)
So if you had a 30% speed bonus on your commander you would do 30 * (6+.3).
But with this the time isn't accurate. I don't know what I am doing wrong but it's probably something stupid.
My speed commander was out so I had to use a very weak speed commander (8.1%)
I did 287/10 = 28.7
Then I did 28.7 * (6+.081) = 174.5247
I divided by 100 = 1.745247 and added 1 and then multiplied by the speed of the unit. I used a very slow unit to test the lower extreme.
So I did 2.745247 * 19 = 52.159693
I then used Cat's formula and did: [100/(52.159693)] * 287 and got 532.978597094
I divided that by 60 to get the hours and got this. 8.88297661824
I took the decimals and multiplied by 60 to get 52.9785970944 (53 minutes)
But when I tested it in the game it was 8 hours : 27 minutes
Sorry for the long post and I edited the formula.
All of this was done through attacking and not supporting.
I want to tackle each percentage by itself.
[1734430]
cat402 [None]
:: April 3, 2014, 9:26 p.m.
How did you get the formula in the begginign?
[1734455]
dueltheabdul (INT1) [None]
:: April 3, 2014, 10:03 p.m.
How did you get the formula in the beginning?
I just made what Porky said/did into a formula.
One of Porky's earlier posts explains how the horses work.
[1734459]
cat402 [None]
:: April 3, 2014, 10:05 p.m.
Double post bug
[1734495]
Lord Porky [None]
:: April 3, 2014, 11:14 p.m.
Abdul, you're multiplying by the Commander bonus in that formula. Rather than adding it to the Horse bonus and then multiplying by D/10, the Commander bonus should just be added in once.
[1734593]
dueltheabdul (INT1) [None]
:: April 4, 2014, 2:02 a.m.
Lord Porky wrote: »Abdul, you're multiplying by the Commander bonus in that formula. Rather than adding it to the Horse bonus and then multiplying by D/10, the Commander bonus should just be added in once.
I don't see what you are pointing out.
I did add the Commander bonus to the Horse bonus. The commander bonus has to be divided by a 100 before being added to the Horse bonus.
It is added only once.
[1734675]
Lord Porky [None]
:: April 4, 2014, 5:44 a.m.
dueltheabdul wrote: »I did add the Commander bonus to the Horse bonus. The commander bonus has to be divided by a 100 before being added to the Horse bonus.
It is added only once.
Abdul, you are making an old man's head spin.... ^^
One thing I haven't tested is if the Commander bonus is added to the base speed before the Horse bonus is applied, or afterward - that obviously would make a difference.
Correct me if I'm wrong here:
S= (D/10) *(H+ B/100)+1 * s
B/100 is to correct for the Commander bonus being in percent, correct? That is, we say '90/90' but it's really .90/.90.
On the multiplication, D/10 gives the number of times the Horse speed bonus is added, so to multiply H by that quantity is correct, I certainly think.
But by adding B/100 to H, and then multiplying by D/10, you are multiplying the Commander bonus as well as the "every 10 spaces Horse bonus." If the distance is 10, it will work out right, because then the multiplier is 1.
But if D/10 is less than 1, then you'll be reducing the Commander bonus, and if it's more than 1, then you're increasing it.
S= [(D/10) * H] + 1s + (B/100 * s)
How about that? (If it needs more work, it wouldn't be surprising - I've been drinking and watching TV for hours....)
[1734686]
therealsporer (US1) [None]
:: April 4, 2014, 6:21 a.m.
drunk math is the best math
[1734693]
Lord Porky [None]
:: April 4, 2014, 6:31 a.m.
therealsporer wrote: »drunk math is the best math
"If one drink is good, then ten are great."
[1734806]
dueltheabdul (INT1) [None]
:: April 4, 2014, 11:03 a.m.
Lord Porky wrote: »Abdul, you are making an old man's head spin.... ^^
One thing I haven't tested is if the Commander bonus is added to the base speed before the Horse bonus is applied, or afterward - that obviously would make a difference.
Correct me if I'm wrong here:
S= (D/10) *(H+ B/100)+1 * s
B/100 is to correct for the Commander bonus being in percent, correct? That is, we say '90/90' but it's really .90/.90.
On the multiplication, D/10 gives the number of times the Horse speed bonus is added, so to multiply H by that quantity is correct, I certainly think.
But by adding B/100 to H, and then multiplying by D/10, you are multiplying the Commander bonus as well as the "every 10 spaces Horse bonus." If the distance is 10, it will work out right, because then the multiplier is 1.
But if D/10 is less than 1, then you'll be reducing the Commander bonus, and if it's more than 1, then you're increasing it.
S= [(D/10) * H] + 1s + (B/100 * s)
How about that? (If it needs more work, it wouldn't be surprising - I've been drinking and watching TV for hours....)
Sorry for that
I also made a mistake with my version.
It should have been
S= [(D/10) *(H+ B/100)/100 +1] * s
Okay so I tested the last part of your formula and it works fine without the Horse bonus.
The problem is that both the Horse Bonus and Commander bonus (both alone) have to be multiplied by the speed.
I tried multiplying both the Horse bonus part and the commander bonus part by the speed, but the time was greater than what it should be.
[1740934]
pajeg2 (GB1) [None]
:: April 12, 2014, 5:23 p.m.
mantle without horse
mantle do 15 miles per hour
15*0.6=9
mantle do 9 km per hour
60/9=6.67
(10*6.67)/1=66.7
mantle with gold horse
(20*6.67)/(1+0.013*20)=105.71
mantle with rubies horse and 80 speed commander
((10*6.67)/(1+0.022*10)/(1+0.eight)=30.37
mantle do 15 miles per hour
15*0.6=9
mantle do 9 km per hour
60/9=6.67
(10*6.67)/1=66.7
mantle with gold horse
(20*6.67)/(1+0.013*20)=105.71
mantle with rubies horse and 80 speed commander
((10*6.67)/(1+0.022*10)/(1+0.eight)=30.37