Doing rocket/objects/bodies statistics calculations on paper vs. mods

[SalehRam]

Hello!

I have been wondering about manually calculating the rocket/objects/bodies statistics on paper rather than using mods.

I love KER, but I am looking for a way or a style later on where I don't rely on it to design my rockets... (And maybe later if I got the time, make small plugin that only shows the required information from the rocket to take them and do the TWR, dV, burn time, etc... calculations manually).

I tried to make the calculations on a sheet, but they were way off the actual numbers shown in KER. I had a rocket in KER showed 11k dV, while on my sheet it was showing 14k dV, so I was wondering what KER takes into account when calculating the numbers?

The way I did it was to calculate the stages I know will be in atmosphere based on the Isp in atmosphere for the engine, then for vacuum stages, I used the Isp for vac.... Is it how KER do the calculations then takes the average or am I wrong?

I am looking to get the calculations correct as I want to remove KER and just use my own calculations and to improve my math as part of my math re-learning program

Also, I am looking for these equations:

1. The set of equations to calculate launch profiles and ascent paths for rockets, also planetary transfers and windows.
2. One other really PITA thing I have is determining the landing trajectory of an object. I use the mod Trajectories which is awesome, but again I want to do it myself...

 

Really appreciate your feedback!

[Plusck]

The very best place I've seen for all the nuts and bolts is http://www.braeunig.us/space/

However, KER doesn't always get the numbers quite right. One thing it really doesn't manage is drop tanks - it systematically understates the dv that you can get out a ship with droppable tanks.

On the other hand, I dont know how well it works out concurrent burns. For example, if you have SRBs and LF engines burning at the same time, you need to know exactly how long they will be burning and do two separate rocket equations: one for the combined ISP / burn time until SRB runs out / initial ship mass and mass of LF used during that time, and a second one for the LF engines alone from that point onwards. Considering the information that KER gives you, I would assume that it does this calculation correctly, but you might easily miss a step or two on paper.

[Snark]

Congratulations on the motivation to do it "old school"! 

2 hours ago, SalehRam said:

I tried to make the calculations on a sheet, but they were way off the actual numbers shown in KER. I had a rocket in KER showed 11k dV, while on my sheet it was showing 14k dV, so I was wondering what KER takes into account when calculating the numbers?

Calculating KSP numbers for dV is pretty straightforward, though if you have a large number of stages it can get tedious.  Basically, what you do is to calculate the dV numbers separately for each stage, then add the numbers together.  I have no idea whether you're calculating this correctly or not, since you don't describe your process. 

Calculating the dV for one stage is a matter of applying the rocket equation:

1. Find the "wet mass" of the stage, in tons:  that is, its total mass including all fuel and all subsequent stages, before burning any of the stage's fuel, but after staging away the empty remnants of any previous stages.
2. Find the "dry mass" of the stage, in tons:  that is, the mass after burning all of that stage's fuel, but before you stage away the empty tanks/engines/whatever.
3. Divid the wet mass by the dry mass; this is the mass ratio for that stage
4. Take the natural log ("ln" button on your calculator) of the mass ratio
5. Multiply by the I_sp of your engine, in seconds.  (If you have multiple engines that all have the same I_sp, just use that I_sp.  If you have multiple engines simultaneously burning that have different I_sp values from each other, then it's more complicated.)
6. Multiply by 9.81 m/s²(this is Kerbin surface gravity; this step has nothing to do with where your rocket is located, it's  needed because the I_sp values that KSP reports are normalized by this amount)
7. This is the dV for that stage, in m/s

The above is the "simple" case.  If you're running multiple engines simultaneously that have different I_sp, or you have "overlapping" stages where one stage starts burning before the last stage has finished, then it gets more complicated.

The easy way to do the above is to calculate the dV for each stage as you build your rocket from the top down in the VAB.  I like to use the "notes" section of the rocket in the VAB to record dV values, e.g. something like this:

Stage 0:  2136 m/s
Stage 1:  1820 m/s
Stage 2:  1520 m/s

2 hours ago, SalehRam said:

The way I did it was to calculate the stages I know will be in atmosphere based on the Isp in atmosphere for the engine, then for vacuum stages, I used the Isp for vac....

Actually, you'd do better if you did something like this:

• For the first stage (i.e. the one you lift off the launchpad with), take the average of its atmospheric and vacuum I_sp.
• For all subsequent stages, just use the vacuum I_sp (even if they're still in atmosphere).

Reason:  Atmospheric pressure drops off fast with altitude.  By the time you're at 4000 m or so, you're already at around 0.5 atmospheres, i.e. you're already halfway to vacuum!  And by the time you're at 10 km, the atmospheric pressure is down to around 10%, meaning that you're 90% of the way to vacuum already, and your engines' I_sp will be much closer to their vacuum values than to atmospheric.  By the time you're above 20 km, atmospheric pressure is under 1% of sea level and your I_sp is just about indistinguishable from vacuum.

Exactly how it works out will depend on your ship design, of course, but chances are good that your first (launchpad) stage will take you up to well above 4 km altitude, so you should come pretty close if you use the average of its atmospheric and vacuum values.  Every stage beyond the first one is effectively running in a near-vacuum, so just use the vacuum value.

2 hours ago, SalehRam said:

The set of equations to calculate launch profiles and ascent paths for rockets

That one's really hard.  It critically depends on a lot of design-specific things including your TWR (which varies as you burn fuel and stage) and your atmospheric drag and lift (which is totally dependent on your craft's shape).  So working it out by hand is gonna be a bear.  You'll probably do better just to practice and develop an instinctive feel for when to tip over and by how much.

Designing your rockets to have a consistent TWR can help with that.  For example, I religiously keep all my rockets to a launchpad TWR of 1.5, which means that they all tend to have a pretty similar profile when launching, and therefore I get lots of practice in optimizing that.

2 hours ago, SalehRam said:

planetary transfers and windows.

This one's simpler.  Let's say you're going from planet A to planet B.

1. Take the average of A's orbital radius and B's orbital radius.  This is a, the semimajor axis of your transfer ellipse.
2. Calculate the time taken to do the transfer.  This equals pi, times the square root of (a³ / GM), where GM is the standard gravitational parameter of the primary body the planets are orbiting (e.g. the Sun).  You can get that number off the KSP wiki, or in-game by focusing the map view on the body in question and opening the info panel.
3. Now you need to know how far the target planet B will move during that time.  (I'm assuming B's in a near-circular orbit that's not inclined too much from A's).  Divide B's orbital period by the transfer time you calculated in step 2, and multiply by 360.  That's how many degrees B will move during that time.
4. Add 180 degrees to the number from step #3.  If you get a number >360, take the modulus 360.  That's what the phase angle between A and B needs to be when you launch from A.  If it's <180, then A will be ahead of B when you launch.  If it's >180, then A will be behind B when you launch.

You can use http://ksp.olex.biz to conveniently check your calculations here. 

2 hours ago, SalehRam said:

One other really PITA thing I have is determining the landing trajectory of an object. I use the mod Trajectories which is awesome, but again I want to do it myself...

Again, this is hard.  The curve will change as you burn fuel, it'll depend on your varying TWR.  I would say this is impractical to do by hand.  Again, I just use practice and instinct for this one. 

 

Incidentally, if you're not averse to getting some mod assistance, but want much less help than KER, then may I suggest this little mod that I wrote:

It gives better "burn time" numbers, and also provides a rough "time to impact" indicator which is useful for landings on vacuum worlds, and some other small goodies, but that's about it.  It has essentially no UI, and (by design!) doesn't calculate dV for you or anything like that, so you'll still need to pull your calculator out when you're desigining your ship.

[GoSlash27]

I started out doing all the calculations by hand. Once I was comfortable with the math and was confident that I understood all of it, I made a spreadsheet that does the number crunching for me.

 The big advantage of learning the math yourself instead of relying on mods is that it gives you the ability to mathematically design stages instead of just evaluating stages you've already built. Like... with KER you can build a rocket in the SPH and it will tell you what DV and T/W it will produce. But if you understand the math, you can turn the whole process backwards and let the math tell you exactly which engine is best and how much fuel/tankage for your desired DV, T/W, and payload. It really simplifies everything.

As for the transfer windows and mission planning, the Vis- viva equation is the most important thing to understand. Same thing; I worked it by hand and eventually created a spreadsheet to do it for me. Lots of missions require DV budgets that don't appear on any maps.

Best,
-Slashy

Edited March 2, 2016 by GoSlash27

[SalehRam]

 @Plusck and @Snark and @GoSlash27 Thanks a lot for your great replies... They cleared lots of points and confusions I had before...

Quote

 The big advantage of learning the math yourself instead of relying on mods is that it gives you the ability to mathematically design stages instead of just evaluating stages you've already built. Like... with KER you can build a rocket in the SPH and it will tell you what DV and T/W it will produce. But if you understand the math, you can turn the whole process backwards and let the math tell you exactly which engine is best and how much fuel/tankage for your desired DV, T/W, and payload. It really simplifies everything.

That is the main reason why I want to do the math myself... I did it few days ago and I enjoyed it really, adding to that the greater depth it took me into the design I was making, knowing why this engine and why that specific part instead of this, was really enjoyable, so I want to do more of these...

 

Edited March 2, 2016 by SalehRam
Fixing mentions