How does velocity affect specific impulse, & how does velocity correlate with altitude?

[KocLobster]

As with every question I bring to this forum, I research beforehand, to the best of my ability, to try and find an answer through google and previously asked & answered questions on this forum. Unfortunately, a lot of times I do not produce a satisfactory answer or one that I can comprehend; thankfully, everyone here is immensely helpful.
 

Like the title says, I'm trying to figure out how velocity affects specific impulse, if at all. If I am going faster or slower, how does this impact how efficient my fuel consumption is? Does it even make a difference? I have been of the impression that it doesn't affect lsp at all, or at least in any measurable manner, but I wanted to confirm this.
 

My second question, which is slightly related, is how does velocity correlate with altitude? Specifically, what are the approximate ideal speeds you should be flying at, at given altitudes? I assume that the farther away you are from these guidelines, the less efficient you are, and that your fuel consumption will increase/lsp will decrease. Is this actually the case? I have been following what I have perceived to be roughly correct guidelines: generally, I shoot for not going any faster than 300 m/s until at least 7km above Kerbin (when you enter the next section of atmosphere with thinner air). After this point, I honestly don't have any idea what speeds are appropriate at what altitudes, or if they even matter in the first place. Speaking in general again, I usually run at full throttle the entire time, as long as I kept my TWR at ~1.7, or at least below ~2 (at sea level, or SLT).

I don't know if these values/guidelines/assumptions/understandings are accurate, or even correct. I do know that they have worked for me pretty well so far, and at a minimum, they get me from point A to point B with roughly the same amount of dV (or less!) as that listed in most dV maps/calculators (using the most strict settings & least amount of fuel wasted). Thanks for you help!

[Snark]

Your Isp is unaffected by velocity.  It varies with atmospheric pressure, but other than that, it's a constant.

As for ideal speed:  if you mean "ascent through the atmosphere to space", then you want to be going right at terminal velocity the whole way, to get the best tradeoff between gravity losses and drag.  Unfortunately nobody can tell you a simple answer to how fast terminal velocity is, since it totally depends on your ship design.  On Kerbin, though, it's not much of an issue-- unless you have a TWR that's crazy high, you'll never get close to terminal velocity because it'll rise faster than your ship's speed does as you climb.  So basically, don't worry about it.  Just pick a reasonable launchpad TWR (I like to use 1.5, myself), and do an efficient gravity turn, and you're good to go.

(The terminal velocity thing does make a difference on Eve, since you have to climb straight up for a long time before starting the gravity turn.)

If by "ideal flying speed" you mean just "flying along as an airplane for long distance travel," you'll need someone else to help you with that, I'm not an airplane guy. 

[KocLobster]

44 minutes ago, Snark said:

Your Isp is unaffected by velocity.  It varies with atmospheric pressure, but other than that, it's a constant.

As for ideal speed:  if you mean "ascent through the atmosphere to space", then you want to be going right at terminal velocity the whole way, to get the best tradeoff between gravity losses and drag.  Unfortunately nobody can tell you a simple answer to how fast terminal velocity is, since it totally depends on your ship design.  On Kerbin, though, it's not much of an issue-- unless you have a TWR that's crazy high, you'll never get close to terminal velocity because it'll rise faster than your ship's speed does as you climb.  So basically, don't worry about it.  Just pick a reasonable launchpad TWR (I like to use 1.5, myself), and do an efficient gravity turn, and you're good to go.

(The terminal velocity thing does make a difference on Eve, since you have to climb straight up for a long time before starting the gravity turn.)

If by "ideal flying speed" you mean just "flying along as an airplane for long distance travel," you'll need someone else to help you with that, I'm not an airplane guy. 

You know everything!

Yeah, you understood what I was asking, that is good to know. How exactly does atmospheric pressure affect lsp?

For ideal flying speed, I wasn't actually referring to planes. I'm not an airplane guy either, I have yet to understand how in the world space planes work and all of my attempts, regardless of how many quality tutorials I look at, never work very well. I was referring only to rockets, and generally at what altitudes should my velocity be... For example, I believe it's ideal to not exceed about 300m/s until after the ~7km mark. After that I don't know. But if I understand you, you kind of already answered both questions with one answer?That ideally I would be going at terminal velocity the whole way?

[Snark]

14 minutes ago, KocLobster said:

How exactly does atmospheric pressure affect lsp?

In general, higher pressure = crappier Isp.  Exactly how much depends on the engine.  Some engines (the "atmospheric" engines, like Swivel and Skipper) lose only a little bit of Isp in atmosphere.  Others, the so-called "vacuum" engines (like Terrier, Poodle, and Rhino) have much worse Isp in atmosphere, so you should never use those on the launchpad.

Lowered Isp means they generate less thrust while still consuming the same amount of fuel.

To see the effect of atmosphere on Isp, you can look at the descriptive info for the engine in the "parts" tab of the VAB or SPH.  The two numbers of interest are "Vac" (vacuum) and "ASL" (atmospheric, sea level) Isp.  You can also see these numbers on the KSP wiki for engines; they're the "vac" and "atm" columns for Isp, over on the right side of the table, and you can sort by them if you like to see how the engines stack up.

Bear in mind that atmospheric pressure drops off fast with altitude-- by the time you're at 10-12 km, you're already down to only around 10% of sea-level pressure, which means that engines will be getting close to vacuum Isp by that time.  So atmospheric Isp is really about climbing those first 10 km or so..

14 minutes ago, KocLobster said:

I was referring only to rockets, and generally at what altitudes should my velocity be... For example, I believe it's ideal to not exceed about 300m/s until after the ~7km mark. After that I don't know. But if I understand you, you kind of already answered both questions with one answer?That ideally I would be going at terminal velocity the whole way?

Ideally, yes.  However, in principle, that's impractical on Kerbin, because you'd have to accelerate so fast to get up to terminal speed, you'd be carrying more engine than you need, which is itself an inefficient thing to do.

Therefore,  your best strategy is generally to make your rocket as streamlined as you can, pick a reasonable launchpad TWR (I like 1.5, personally), and go with that.  Unless your rocket is really draggy and awkwardly shaped, you'll be below terminal velocity all the way and won't need to worry about it too much-- just make sure you have an efficiently-shaped gravity turn and are tipped over by around 45 degrees at around 10 km.

 

[OhioBob]

@KocLobster,

I agree with everything @Snark just wrote.  The only difference is that I prefer a slightly lower liftoff TWR, anything in the 1.3-1.5 range is acceptable.  For the second stage I typically like something in the 1.1-1.3 range.  Ideally, I want my stage 1 + stage 2 TWR to be equal to 2.6.  From my personal experience, I like the way that performs.

For me, I rarely even look at my velocity during a launch.  Since I try to build all my rockets to a set standard, I get similar performance no matter what I'm flying.  Therefore, I just watch my pitch, altitude, and apoapsis.  Like Snark, I want my pitch to be 45 degrees at 10-12 km.  I like to be horizontal by 35-40 km.  And I like to kill the engine at about 50-55 km, when my apoapsis has reached 75-80 km.  If I do that, then I get a good launch.  Other than at engine cutoff, I can't tell you what my speed is at any given altitude because I honestly don't know.

 

Edited March 21, 2016 by OhioBob

[Plusck]

2 hours ago, KocLobster said:

How exactly does atmospheric pressure affect lsp?

For the real reasons why, wikipedia has a number of good articles such as this one.

Basically, the violently exploding exhaust gases provide thust as they expand and are accelerated out the back of the nozzle. Without a nozzle, they would expand in all directions and only very little of that expansion would be useful for the rocket. As they expand, the pressure of the exhaust gas decreases and its velocity increases. The nozzle follows the curve of expansion and therefore directs all the exhaust in the same direction, ensuring uniform acceleration away from the rocket and therefore, maximum thrust.

When atmospheric pressure increases, the gases cannot expand to fill the nozzle because of that external pressure. Since they cannot expand as much, they also cannot be accelerated to such high speeds. Rocket engines therefore have to make compromises to work well in the atmosphere, and this reduces their efficiency in a vacuum. A very good vacuum engine is therefore, by definition, a poor atmospheric engine.

The exception to this rule is (or rather "should in future be") the aerospike, which allows for a very long virtual expansion bell without actually enclosing the exhaust in a bell, and should therefore allow very good vacuum performance without suffering so much in the presence of an atmosphere.

[OhioBob]

2 hours ago, Snark said:

Your Isp is unaffected by velocity.  It varies with atmospheric pressure, but other than that, it's a constant.

This is absolutely correct in principle, and in KSP.  However, in real life there can be very small changes in Isp resulting from high acceleration or shifts in the mixture ratio.

Mixture ratio (MR) is the ratio of oxidizer to fuel. Changing the MR effects the combustion characteristics, such as the flame temperature and the molecular weight of the exhaust gases.  Therefore, a change in MR changes an engine's specific impulse.  Although an engine is typically designed to operate at a specified mixture ratio, the mixture ratio can shift slightly during flight if the respective flow rates of oxidizer and fuel change.

High acceleration can also alter the flow rate of oxidizer and fuel.  Under high g-loads, the liquid pressure upstream of the turbopumps is increased, which can increase the propellant flow rate to the engine.  Clearly a higher propellant flow rate increases thrust, but it can also change Isp because of a higher combustion chamber pressure.

Both of these effects are usually pretty small, and in KSP they are non-existent.  I just thought I'd mention as a side note in case anyone is interested.

In some cases, mixture ratio is changed intentionally, which can produce fairly significant changes in Isp.  One example is the Saturn V, in which both the F-1 and J-2 engines had a "propellant utilization subsystem" that monitored the remaining oxidizer and fuel and shifted the MR near the end of the burn to assure simultaneous depletion of oxidizer and fuel.  In the case of the J-2 engine, the shift was achieved by changing the position of a valve controlling the flow of oxidizer to the engine.  The PU shift decreased the oxidizer flow rate, resulting in a pretty dramatic decrease in thrust.  Although the thrust decreased, the Isp actually went up by several seconds.

[Padishar]

14 hours ago, Snark said:

Your Isp is unaffected by velocity.  It varies with atmospheric pressure, but other than that, it's a constant.

This is true for all the (stock) rocket engines (which seems to be the main focus of your question) but the various jet engines do vary the thrust with the velocity which indirectly affects the effective Isp (Isp = F / (g * dm/dt)).  E.g. the thrust of the basic jet engine falls off almost completely above mach 1 but it still uses the same amount of fuel per second for the same throttle position.  Similarly, the turbojet has quite low thrust when stationary, really gets going once you get up above mach 1 and then falls off again at higher speed.  This will become an important consideration if/when you start trying to build planes and, especially, spaceplanes.

[wumpus]

Don't touch that throttle!

As long as you are pointed in the right direction (a big if) and you aren't on Eve, you are rather unlikely to exceed your terminal velocity.  You might want to throttle down if you just can't turn the beast (unlikely with a takeoff TWR of 1.5), but it will only make your ascent less efficient (due to gravity losses).

Remember: TWR of 1.5 means wasting 66% on gravity, 1.3 means 77% lost to gravity.  Note building a rocket with much higher TWR runs into all sorts of different problems (control issues, high trust engines are heavier giving more dry mass, instability issues are amplified) so getting too close to 2.0 isn't the answer either.  The point is that if you already built your rocket with a certain amount of thrust, you shouldn't lower it at *all* for "efficiency" issues, but with higher thrust (these issues become obvious around 1.7 and beyond) you might have to lower your thrust if you want any kind of pitchover (don't count on *ever* doing a normal gravity turn with a high thrust rocket).

And of course, on an airless moon (or Moho), there is zero reason to limit TWR (as long as it doesn't cut into delta-v).  Just pop up, turn as sideways as you dare (unless on Tylo.   Then you are stuck with a proper gravity turn) and hit full thrust.  Limiting them on the way down is often done for an more controlled (and often more efficient) landing.

Spoiler

Note: after experimenting with limiting overpowered SRBs heaving second stages into to orbit, I noted that efficiency peaked at a TWR of 2.0, and a TWR of 1.8 was fairly close (with practice I suspect I could have found a turn that the 1.8 rocket could outperform the 2.0 rocket).  Efficiency of the 2.1 rocket (which hit something like a TWR of 6 or 7 while still in the atmosphere) started back down.  Also note that when using kicker based rockets, they tended to explode if launched with a TWR of 2.1 (due to heating on the way up).

While I expected this experiment to vindicate high thrust rockets, I eventually realized that I was dragging around far too much mass to generate the excess thrust and could only claim the folly of reducing thrust via throttle and not by proper engine choice.

 

[Nich]

Vacuume engines create shockwaves in the bell when run in atmosphere because they are over expanded.  These shock wave reduce the exit velocity from super sonic to subsonic

[Warzouz]

14 hours ago, OhioBob said:

@KocLobster,

I agree with everything @Snark just wrote.  The only difference is that I prefer a slightly lower liftoff TWR, anything in the 1.3-1.5 range is acceptable.  For the second stage I typically like something in the 1.1-1.3 range.  Ideally, I want my stage 1 + stage 2 TWR to be equal to 2.6.  From my personal experience, I like the way that performs.

...

Adding TWR of various stages makes no sense. TWR is also lower on the pad because of thrust being reduced. With an average engine (with a Mainsail, a 1.5 TWR vac rocket will end at 1.4 TWR asl. Thrust rises very fase with pressure/altitude.

As a reminder Saturn V had a TWR around (Stage 1=) 1.17 asl, (Stage 2 and 3 =) 0.6 vac

[Snikersnee]

Thought I'd put this here if you need it. For me I usually throttle all the way up on launchpad, then, after liftoff, I throttle as far down as I can, with the ship still accelerating. As the rocket goes up , I can throttle down because less atmo pressure and higher velocity. Don't know how efficient it is but it saves a ton of fuel with solid rocket boosted stages.

[Snark]

26 minutes ago, Snikersnee said:

Thought I'd put this here if you need it. For me I usually throttle all the way up on launchpad, then, after liftoff, I throttle as far down as I can, with the ship still accelerating. As the rocket goes up , I can throttle down because less atmo pressure and higher velocity. Don't know how efficient it is but it saves a ton of fuel with solid rocket boosted stages.

Regarding "solid rocket boosted stages":  I take this to mean that you're launching with SRBs and liquid-fueled engine together?

In that case:  yes, throttling down on the liquid-fueled engine as soon as possible is a good idea.  SRBs have a much worse Isp than liquid-fueled engines do, and for optimizing your dV, you want to burn your worst-Isp fuel first.  So in general you want to spend as little liquid fuel as possible until the SRBs are exhausted.

[KocLobster]

10 minutes ago, Snark said:

Regarding "solid rocket boosted stages":  I take this to mean that you're launching with SRBs and liquid-fueled engine together?

In that case:  yes, throttling down on the liquid-fueled engine as soon as possible is a good idea.  SRBs have a much worse Isp than liquid-fueled engines do, and for optimizing your dV, you want to burn your worst-Isp fuel first.  So in general you want to spend as little liquid fuel as possible until the SRBs are exhausted.

Glad I had the right idea then. I knew I generally need to manually lower my TWR at launch, but wasn't sure if I was doing it the right way. Glad I was, thanks

[wumpus]

3 hours ago, Snark said:

Regarding "solid rocket boosted stages":  I take this to mean that you're launching with SRBs and liquid-fueled engine together?

In that case:  yes, throttling down on the liquid-fueled engine as soon as possible is a good idea.  SRBs have a much worse Isp than liquid-fueled engines do, and for optimizing your dV, you want to burn your worst-Isp fuel first.  So in general you want to spend as little liquid fuel as possible until the SRBs are exhausted.

Note that in general this is right, but the specifics can get hairy.

The big catch here is that if you assume the SRBs are providing >1 g of thrust (whatever you do, don't throttle the SRBs, replacing SRBs with liquid fuel is [nearly] always wrong).  Assume the following rocket: SRBs provide ~1.25 of TWR, Liquid boosters provide ~.5 of TWR (and they roughly scale upward during flight, but maintain similar ratios).

• 1 g gets lost to gravity.
• The SRBs provide roughly .25g of vertical acceleration (even kickers rarely finish the gravity turn) with an Isp of 195s.
• The liquid boosters provide .5g of vertical acceleration (unless throttled down) with an Isp of 285s.

The kick here is that while you may appear to be saving 33% of your fuel by using the less efficient fuel first, the SRB is wasting 4/5 of its fuel fighting gravity and the liquid rocket doesn't.  I'd guess that as long as the ratio of the Isp of the fuels is less than (1-TWR), then things get pretty complicated.  Note that the TWR increases as the rocket climbs, so eventually throttling likely becomes obviously efficient.

I'd suggest experimenting by launching with and without throttling.  I found no real difference, except the chance to botch my steering while adjusting my throttle, but that might have been due to my style of rocket design and launching curves.

[OhioBob]

3 hours ago, Warzouz said:

Adding TWR of various stages makes no sense. TWR is also lower on the pad because of thrust being reduced. With an average engine (with a Mainsail, a 1.5 TWR vac rocket will end at 1.4 TWR asl. Thrust rises very fase with pressure/altitude.

Adding the TWR together isn't a hard and fast rule, it's just that when I can I tend to go toward the lower end of my preferred TWR range on the second stage if the first stage's TWR is toward the higher end of my preferred TWR range, and vice verse. This produces a more consistent total burn time and average acceleration during ascent.  I feel this gives me greater consistency in my ascent profile so that all my rockets fly about the same.  When both stages have low TWR, or when both stages have high TWR, I find I have to fly the rockets differently and I don't get the same consistent ascent trajectory that I like.  When a rocket doesn't behave as I'm accustomed to, I have a tendency to get outside of my preferred ascent corridor and I sustain greater steering losses.  In a perfect world, both my first and second stages are right in the middle of the preferred TWR range.

[Plusck]

9 hours ago, KocLobster said:

Glad I had the right idea then. I knew I generally need to manually lower my TWR at launch, but wasn't sure if I was doing it the right way. Glad I was, thanks

Eerm, not quite.

As some of the other posts here show, the exact right way to do things is somewhat complicated.

What is indisputable is that you want to get up to speed as fast as possible. A TWR of 1 means you are spending all of your fuel merely keeping pace with gravity, and that is a collossal waste of time and energy.

Also indisputable is that any time spent at less than 100% of available thrust is time that you're hauling engines up for nothing.

However, in the lower atmosphere you have to go a bit slower because you can't head horizontally (speed equals heat equals death) and you can't turn against the airflow (you flip, break up and die) but you want to turn gradually in an arc that'll get you horizontal at exactly the right time.

You'll have noticed that @Snark and @OhioBob don't have quite the same view on this, and mine is significantly different to both of them: I give greater importance to those two "indisputable" aspects and that means starting at absolute maximum thrust to get up to speed and off at an angle. If speed in the lower atmosphere gets too high, I throttle back.

The trouble is that there is no easy way to know who is "right". I'm pretty sure my approach minimises gravity losses compared to their methods, but I suspect OhioBob's approach is more efficient in terms of cost for the build and overall fuel usage, while Snark's approach looks (to me) like it falls between the two.

Still, there is a problem with "manually lowering TWR on launch", which is that you must therefore be carrying more engine than you need, which means more weight. Manually lowering TWR means that you are giving a greater percentage of your thrust to gravity. In the meantime, manually lowering your thrust on engines which suffer from being at sea level (such as the Swivel, Skipper or to a lesser extent the Mainsail) will allow more efficient use of your fuel at altitude.

So yes and no, basically : D

[Warzouz]

@Plusck, you're right, there is no real one-way efficient launch since 1.0. That's nice. Flying a rocket vastly depends on how it's designed. Before 1.0, it was always the boring "go straight and turn 45° at 10k" : you couldn't really miss a launch.

[Padishar]

20 hours ago, wumpus said:

(unless on Tylo.   Then you are stuck with a proper gravity turn)

Why are you?  With a local TWR of only 1.5 you can pitch over to 45 degrees and not fall back down (a TWR of 2 lets you pitch over 60 degrees) and, as you pick up horizontal speed you can pitch over more.  You need to get high enough to avoid high terrain but you certainly don't need to do anything like a "proper" gravity turn.

[wumpus]

1 hour ago, Padishar said:

Why are you?  With a local TWR of only 1.5 you can pitch over to 45 degrees and not fall back down (a TWR of 2 lets you pitch over 60 degrees) and, as you pick up horizontal speed you can pitch over more.  You need to get high enough to avoid high terrain but you certainly don't need to do anything like a "proper" gravity turn.

Er, yes.  Presumably you would quickly turn from 45 (preferably steeper) to 90 as your velocity increased.  That and that gravity seems to be about half of Kerbin's means you should be able to manage local TWRs higher than 2 or so (try for more).  While it technically will be a gravity turn, it will appear a highly abbreviated one (of course you could say the same for Minmus, but a pure sideways course (assuming mostly flying over flats, you don't want to become geography) is close enough to not worry about any fuel being wasted).

[KocLobster]

@Plusk

This is a great post and explanation, thank you. Unfortunately, it does leave me slightly confused which way I should go depending on my craft.

[OhioBob]

On ‎3‎/‎22‎/‎2016 at 10:03 PM, Plusck said:

Still, there is a problem with "manually lowering TWR on launch", which is that you must therefore be carrying more engine than you need, which means more weight. Manually lowering TWR means that you are giving a greater percentage of your thrust to gravity. In the meantime, manually lowering your thrust on engines which suffer from being at sea level (such as the Swivel, Skipper or to a lesser extent the Mainsail) will allow more efficient use of your fuel at altitude.

I like a liftoff TWR in the 1.3-1.5 range, but's that's because I like to pack on the fuel tanks and load up an engine with as much weight as it can handle.  I believe this gives the best cost per ton of payload.  However, I'm sometimes forced into using an engine that delivers a higher TWR than I want because that's all that's available.  In that case I launch using the higher TWR (assuming it's not crazy high).  I never want to thrust limit or throttle back a liquid fueled engine.  There's a big difference between arbitrarily lowering TWR just to hit some number, versus lowering TWR by adding fuel.  If you got it, use it.  The only time I ever consider throttling back a liquid fueled engine is if I have to for control reasons (for instance, the rocket wants to flip or it won't turn unless I throttle back).

[Plusck]

1 hour ago, KocLobster said:

@Plusk

This is a great post and explanation, thank you. Unfortunately, it does leave me slightly confused which way I should go depending on my craft.

Well, thank you : D

The only thing I can think of to simplify the question is to list what you want to do, then what stops you from doing exactly that...

• you want to go as fast, and as horizontally, as possible as early as possible,
• you want to use all of your engines at full thrust all of the time,
• you want to be nearly horizontal by the time you cut your engines

... but...

• you don't want to burn fuel pointlessly in vacuum engines while at sea level
• you don't want to overheat and burn up in the atmosphere
• you don't want to flip
• you don't want to spend a very long time in the middle atmosphere (below the 35km mark), although circularising at this height then basically doing a transfer up to 75km would be ideal if there were less drag and heating going on. By nature, spaceplanes do want to do this because they need air to breathe, which overrides concerns about drag and heating.

So your ideal speed (which is the "question" we should probably get back to) is basically "as high as possible without suffering the adverse effects". What your original post said sounds quite reasonable, but it could be a touch higher than 300 m/s once you get to about 4-5km, especially if your rocket is sleek. If you don't have any exposed temperature-sensitive parts, you can be at 350 m/s at 45° at 6km and get to orbit very efficiently. 

To take an unrealistic example, I recently tried a few tests in sandbox with heating turned down to 0%. My most efficient launches with a stupidly high TWR for a direct-to-Mun trajectory were going at 900 m/s at 8km (angle: 30° above horizon) and 1100 m/s at 10km. This was great for going to the Mun, but would have been inefficient for orbit because I would have needed to coast from about 15km up to a relatively slow orbital Ap, thereby losing all of the benefits of the Oberth effect. Trying to improve on that with a more reasonable ascent profile, I was consistently getting a vacuum-dv-to-orbit figure of about 3000 m/s with just a Skipper, but even without heating I was finding it hard to improve on that: excessive TWR just couldn't help because I still needed to climb some way out of the lower atmosphere to avoid drag (I was getting over 100 m/s drag losses just coasting up from the lower atmosphere), and that TWR was therefore going unused for much of the time.

As OhioBob has pointed out, lower TWR can be more efficient if you consider cost: you certainly need a bit more fuel because of gravity losses, but you can cut down on expensive engines.

And as for throttling back, I agree that it should only be for control, but I do light all my engines off the launchpad (generally giving a TWR close to 2) while getting up to speed and initiating the gravity turn (therefore assisted by thrust vectoring) before throttling back to let the SRBs carry me through the turn and up to 8km or so. I feel (but might not be right) that this is more efficient than just waiting for the SRBs to haul me up, and uses a limited amount of fuel at non-optimal Isp to minimise that grinding, uselessly-vertical-and-fighting-gravity time before I can open up and direct my energies mostly horizontally.