Launch windows - geting the inclination change minimised

[kerbinorbiter]

so, weve all came across this problem how do we calculate orbital launch windows?

so lets say we have a spacecraft in orbit that we want to dock to at an inclination of 51.6 degrees you are at the launch pad so first off we need to find what heading we need to launch towards

for this We will assume:

• That it is day time
• the rocket takes 300 seconds to launch into orbit (5 minutes)
• the target is in an inclined orbit to 51.6 degrees equatorial

 

to find where we need to point we can use this equation 

where

H is the heading

I is the target inclination

H = 90-I

why did i take away 90 from the Inclination because in KSP the poles are aligned to a heading of 0 and the equator is on a line of 90 because thats east and the planet is rotating to an angle of 90 degrees to the poles 

so for 51.6 degrees we compute:

H = 90 - 51.6

and we find that:
H = 38.4

so now the launch window:

WHAT DO WE KNOW?

• The heading we need to launch towards
• The time it takes to launch

WHAT DO WE NEED TO KNOW?

• The rotation rate of the planet
• How much it rotates in the time it takes to launch
• The time that the acsending node comes over the launch site on any given day

HOW CAN WE FIND THIS OUT?

For the rotation rate of the planet 

• Open the nav ball
• click on the speed indicator
• and note the reading on the "orbital" value 

for kerbin this comes to 175 meters per second

now we also need to find the length of one degree on the planet

so we need the planet's diameter

for kerbin that's 1200 Kelometers however the speed of rotation is in METERS per second there is two ways we can go with this

OPTION A: convert the radius into meters 

OPTION B: convert the speed of rotation to KELOMETERS per second

personaly i prefer option A but thats my persional preference

EQUATIONS WE NEED:

• Circumference (Pi * Diameter)
• average speed (Speed = distance/time) 

(INSERT CNTRL ENTER HERE WOOPS BEAR WITH ME EXCUSE MY GRAMMAR)  

Pi * 1,200 = 3769911.1843077518861551720599354

leave that in your calculator and devide that by 360

3769911.1843077518861551720599354/360 = 10471.975511965977461542144610932

so there are 10471.975511965977461542144610932 meters in a degree on kerbin

SPEED = distance/time we know all of these but the distance 

so how long does it take for kerbin to rotate 1 degree?

time = distance/speed

time = 10471.975511965977461542144610932 /175 

after computing this we get: 59.839860068377014065955112062469 seconds

roughly 1 minute

so if it takes 300 seconds to launch a vehicle we devide 300 by 59.839860068377014065955112062469

300 / 59.839860068377014065955112062469 = 5.013380707394703076719838546234

kerbin will rotate: 5.013380707394703076719838546234 degrees while launching 

WHEN DO WE LAUNCH?

When the target is at a distance of:

the orbit + 10471.975511965977461542144610932* 5.013380707394703076719838546234 

we get 52500 meters 

IF we are launching to a target at 200 KM we need to launch when it is at a distance of 252,500 meters at a heading of 38.4 degrees and by the time you have read this you probably have missed the launch window!

 

Edited January 1, 2018 by kerbinorbiter