Ascent Costs of Inclined Orbits | KSP Let's Do The Math

[@MikeAben]

Up Next: Ranges & Signal Strength - kzbin.info/www/bejne/nofHXoqegZmnkJo

[@librainvictus5660]

sir, you are painfully undersubbed and viewed. this much effort and dedication deserves a lot more then 450 views. Who knows, their loss... And im not talking gamewise but physics-wise. This game and these videos can help a lot of students, both highschool and bachelor, to learn and practice these equations.

[@MikeAben]

Thanks a ton! As for the views, I really don't go through any effort promoting the channel, but I have fun making these.

[@coalescence4479]

@@MikeAben You're definitely getting a following though. I absolutely love this content!

[@AdrianColley]

This one was really useful. Thanks!

[@mef9327]

I love these math videos. The dv map is ok for quick reference assuming you enter/leave their exact orbit specifications which is rare for me. I also try to combine missions which often require different altitudes/transfers. I was finally able to put together a spreadsheet so I can plan better than just overkilling my rockets with 30,000 dv (exaggerated). Anyway, I know this is an old video. But, wanted to comment to help the algorithm. You deserve *a lot* more subs and views. *QUICK QUESTION:* When skippable ads play, do you get more if I don't skip? Yours is one of a very few channels I would let the ad play the whole time if it helps.

[@MikeAben]

Thanks for the algorithm bump. Don't worry about watching ads. I could never ask someone to watch more of those than they have to. Spreadsheets rule!

[@brian554xx]

If you launch in the desired direction, you end up traveling along the red arrow. You need to do a little trig to get the correct heading for launch so that you end up going the direction you want.

[@MikeAben]

Definitely.

[@maxjenkinson9870]

2:40 ProGryaaaddee

[@Freak80MC]

Coming back to this after having used your technique of getting to orbit by throttling lower as you go higher and turns out I ended up at one point only using 3300 m/s of dv, 100 less than even the minimum shown on that graph! (though of course this had to happen in a test flight and then I do the actual flight afterwards and somehow use 3700... I guess I'm not very consistent with my ascent profiles)

[@MikeAben]

It's hard to be consistent with ascents. It can vary a lot with different rockets too. I'm still in the habit of budgeting 3600 m/s to reach orbit.

[@Freak80MC]

@@MikeAben Yea, might be a good idea to try to learn that KOS mod to try to program ascent profiles to make it consistent.

[@MikeAben]

@@Freak80MC It's a ton of fun.

[@yue7507]

hey Mike, sorry for asking so many questions. at 7:04 would it be wrong to add the atmospheric drag v to deltaVa and using that value in calculating the resultant delta v? essentially you're adding the 1000m/s value before instead of after edit: and also the same at 8:10

[@MikeAben]

I'm not sure I would use the word "wrong" in this case. As I mentioned at the start of the video, I'm avoiding getting into dealing with aerodynamic forces entirely by simply adding an extra 1000 m/s to overcome drag. I'm not sure how this would be taught in a classroom setting. This is just what I do. My rational for adding it on after is that drag would always be opposite to the direction of motion. As such, the extra delta-v required to oppose drag should be in the direction of motion, ie. the prograde direction. If you look at the diagram at 7:04, that red vector is the prograde direction. In fact, if you calculate the angle at the bottom of the triangle, it will give you the heading you should fly at. This is something I didn't get into here. Maybe something for a future episode. Anyway, the v_drag should be added after calculating the magnitude of the red vector, which is exactly what I did. Adding it before would get a number a little smaller, but honestly, likely not far enough off to worry about.

[@Freak80MC]

At 3:35 wouldn't that 1,002 m/s not only be costs in terms of atmospheric drag but also gravity losses? I think those are the two things you have to take into account affecting your delta v as you ascend into orbit.

[@MikeAben]

The delta-v_a is derived using the vis viva equations which already account for gravity losses. That would be the cost of ascent if Kerbin didn't have an atmosphere.

[@tabbycat6802]

​@@MikeAben This can not be true. The gravity losses means not the pure potential energy, it means losses from accelerating against the gravity field (which you not do in the calculation, but it's neccesary for sure). This loss depends on the TWR as well. Only in the case of infinite thrust you can cancel that out.

[@braddaily8688]

Do you have some ideas on how to set this up in a spreadsheet? Figuring out what angles to input and how to calculate them in a spreadsheet is confusing me.

[@MikeAben]

I actually have a video on making a KSP Spreadsheet - kzbin.info/www/bejne/Zoq3qZyEat1motU I don't do the calculation in this video, but the formula presented at around 9:00 as a spreadsheet formula would be =sqrt(6688800-928800*cos(pi*angle/180)) Multiplying the angle by pi and dividing by 180 converts the angle to radians, which you have not likely covered in school yet. Radians is just a different unit to measure angles in, just like you can measure length in feet or in meters. The cosine function in most spreadsheets needs to be in radians. Good luck. Let me know how it goes.

[@griflet1]

hey, I'm finding these video's really usefull for a big school assignment. We also want to include a gravity slingshot tho. Have you used that in one of your previous KSP video's? if so, could you tell me in what video? thanks a lot

[@MikeAben]

This is the closest I've got. No math, though it wouldn't involve any formulas that I haven't already presented. kzbin.info/www/bejne/ooWbnmuYYt6Se7M

[@griflet1]

thanks, I'll have a look at it when I'm done with the rocket and vis viva equations applied to an earth-jupiter hohmann orbit. I'm not that good at math, so these video's are really helpfull.

[@MikeAben]

Actually, thinking a bit, actually determining the outcome after a gravity assist may be a tougher problem.

[@Unpurist]

Hey mike i typed the vis viva equation for a homein transfer on kerbiy and it gave me a value of 2.9394836 i felt like i did something wrong

[@anxiousseal556]

Hello Mike, what does the Δv1 and Δv2 represent?

[@MikeAben]

This reply may be longer than you expected. The two formulas are the vis-viva equations and I talked about them in much greater detail when I derived them here - kzbin.info/www/bejne/bXLOkp54armCidk - but I will give you the condensed version. To perform a maneuver in space, you need to change your velocity by firing your engines. The amount you need to change your velocity by is called the delta-v (Δv). A common maneuver is moving from a circular orbit to a new circular orbit at a different altitude. This is called a Hohmann transfer and requires two burns. The Δv1 and Δv2 represent the delta-v of these two burns, the first at the lower altitude and the second at the higher. I'm not sure where your experience level is with this stuff and what I've just said may have been over (or under) your head. If things aren't clear, don't hesitate to ask another question. I recently made another video which talks about maneuvers and delta-v without getting into the math - kzbin.info/www/bejne/jZy4YWumjbqDgcU

[@anxiousseal556]

@@MikeAben ah okay, I've watched your another videos (they are super helpful btw thanks! :D). My conclusion is the Δv1 represent Δv needed to launch from the surface of the planet to the desired height and Δv2 is the Δv needed to create an orbit. Is that right?

[@MikeAben]

@@anxiousseal556 Gotcha. Technically, Δv1 is the delta-v of a burn to take me from an orbit right on the surface (imagine if Kerbin were a perfect sphere with no atmosphere and the orbit was just skimming the surface) to an orbit with an altitude of 80 km. Clearly, this isn't what really happens as we are stationary on the surface at the start. That's why I add on the orbital velocity of 2426 m/s (the speed we would need for an orbit with an altitude of zero) and subtract off the 175 m/s we are already travelling due to Kerbin's rotation. Again, 'technically', Δv2 is the burn required to create the orbit at 80 km, but once again that's not really what we do. We are looking at the idealized situation of doing one, instantaneous, horizontal burn on the surface, followed by a second burn at 80 km. So the calculations have to be looked at as a lower bound on the cost. This is talked about in greater detail in episode #6 when I do these calculations for the Mun and Minmus.

[@anxiousseal556]

@@MikeAben nice, thank you Mike!

[@MikeAben]

@@anxiousseal556 You bet.

[@akiraaa_____]

Wait. I haven't played KSP before. And you telling me that Kerbin rotates from East to West ? So the sun would rise from the West ?

[@MikeAben]

No, Kerbin rotates west to east. If I said the opposite, then I mispoke.

[@akiraaa_____]

@@MikeAben ooh I see. One question remaining. In your video you show us how to get the orbit with certain inclination. But how to get into orbit with certain inclination At certain latitude. Do you have any videos on that ?

[@MikeAben]

Sorry, I'm not see where I said Kerbin rotates west. The rotational velocity of Kerbin is 180 m/s [east]; however, we are continually subtracting this vector in our calculations which has me drawing 180 m/s [west] in the diagrams. As we are already on Kerbin's surface moving at this velocity, we subtract Kerbin's rotational velocity from the velocity we require to achieve an orbit. I can see how this can be confusing as I spent little time explaining why this. I talked about it in more detail in the previous video. kzbin.info/www/bejne/l4SrYWqknKeVf7s

[@akiraaa_____]

@@MikeAben yeah silly me. I just realized that I'm putting east and west on the wrong direction. I thought that east is at the left direction. My bad 😂. might check your video now.

[@MikeAben]

@@akiraaa_____ Not yet, no, though it's something to consider.