TWR? Delta V? WTH?

[GoSlash27]

I agree that calculating delta-V by hand is tedious - but only in as much as that you have to take the time to figure up the wet and dry masses; the actual calculation is only difficult if you don't have ready access to a calculator (I mean, can anybody tell me what ln(3.28864685689) is without punching that into a calculator/spreadsheet? Because that would be impressive).

No, *heck* no! haha

Nobody has done that sort of thing with natural logs since back before the American Revolution. Just plain not needed.

Way back when, they'd just look it up in a log table. And never to that many decimal places, since that kind of precision was never needed (something we've forgotten these days).

After someone invented the slide rule, they'd just use that. Then calculators, then computers, then spreadsheets.

But being an electronics guy, I *can* guesstimate base 10 logs in my head with a fair degree of accuracy. All comms electronics techs and engineers pick up that ability over time.

The method to do it isn't the same as what LD describes, but he's talking about a different base.

Having said that, your point is absolutely valid. You don't actually have to know the first thing about natural logs to run this equation. All you have to be able to do is find the button marked "ln" on a calculator and push it. Anybody can do that.

Best,

-Slashy

Edited December 13, 2014 by GoSlash27

[LethalDose]

(I mean, can anybody tell me what ln(3.28864685689) is without punching that into a calculator/spreadsheet? Because that would be impressive).

No, *heck* no! haha

Nobody has done that sort of thing with natural logs since back before the American Revolution. Just plain not needed.

You know how I know you're not keeping up with this thread? I demonstrated how to do this 3 pages ago with factoring and addition takes less than a minute if you know how.

Seriously, start checking your facts. Scientists and engineers estimated these values accurately, by hand, well into the 1980's (I've spoken with my professors in biostatistics that have done this). Your assertion that no one has done this since the American Revolution is preposterous. With a few commonly used natural logs of primes (ln 2, ln 3, ln 5, etc), you can factor out the number and approximate very good answers to logs like this in about 30 secs with practice.

Given about 5 minutes (again, less given some practice), you can calculate two extrema using this method and interpolate a much more accurate answer. It's not exact, but as you yourself said, you don't need that many decimal places.

No tables, no calculators, no slide rules.

It's not impressive, it's basic math. It's just basic math we don't have to do anymore.

Heh, you know it's an interesting parallel with another thread I read about how calculating dV isn't that hard. Ends up calculating natural logs isn't that hard, either.

Why does everyone say that?

Edited December 13, 2014 by LethalDose

[Vanamonde]

Keep the discussion about the subject and avoid criticizing each other personally, please.

[OhioBob]

I definitely agree with those that say a gradual turn is most efficient. When sharp turns are made too much dV is lost in changing the direction of the velocity vector rather than in increasing the magnitude of the velocity vector. To be most effective you want to make sure your pitch is never far from the prograde marker on the NavBall. I like to start my turn shortly after passing 5000 m altitude. I then set my pitch a few degrees ahead of the velocity vector, i.e. near the edge of the circle on the prograde marker. As the prograde marker begins to fall towards the horizon, I continually increase pitch to stay a few degrees ahead of the center of the marker. If I have a well designed rocket and I've maintained good control of my attitude, my pitch should be horizontal at the time of engine cutoff with the prograde marker a few degree above the horizon.

How fast the prograde marker falls toward the horizon depends on TWR. I tend to build all my rocket with similar TWR*, therefore controlling the rate of the turn becomes pretty standard and easy to do. However, if you have very differently designed rockets, the rate of turn can vary quite a bit. If the prograde marker begins to fall too quickly, or not quickly enough, you'll have to adjust your pitch to compensate. To increase the turn rate, increase the gap between your pitch and the prograde marker, and to slow down the turn rate decrease the gap (you may even have to change your pitch to the trailing side of the marker if the turn starts to get out of control and increases too quickly). Also make sure not to end your burn too low in the atmosphere. I usually like to be at an altitude of about 50 km when I end my first burn, with a subsequent circularization burn at my target apoapsis.

The main points are (1) start your turn at about 5-6 km, (2) maintain your pitch close to the prograde marker and avoid sudden large changes, (3) end your burn with the prograde marker at about +3 degrees to the horizon, and (4) be at an altitude of about 50 km at engine cutoff. Stick to these rules and you should have pretty good success. I find that a couple launches with a new rocket is all it usually takes to find the right touch to have a pretty effective and well controlled ascent. BTW, I use the stock game.

* Ideally I like my first stage to have a TWR of about 1.6-1.7 and my second stage about 1.3. Upper stages for orbital maneuvering or transfer orbit injection can be much less, generally <1 is adequate.

[OhioBob]

When sharp turns are made too much dV is lost in changing the direction of the velocity vector rather than in increasing the magnitude of the velocity vector.

To illustrate this point I submit the following:

Here we have a simplified scenario in which we assume a constant acceleration and neglect gravity and drag. In all three cases the rocket produces 3000 m/s delta-v, represented by the black arrows. In example A the rocket makes a 90-degree turn halfway through the burn. In example B the rocket make a 45-degree turn 1/3 through the burn and another 45-degree turn 2/3 through the burn. In example C the rocket makes a smooth constantly bending 90-degree turn. The red arrow represents the resultant final velocity vector. You can see that the more gradual the turn, the higher the magnitude of the final velocity vector.

This illustrates why frequent small turns is far better than sudden large turns. The common technique of going straight up to 10 km and then pitching over 45-degrees is not particularly efficient.