Thoughts regarding twr, delta V, and the best "Kerbal" rocket

[Pacca]

I've been paying much closer attention to delta V, engine weight, and twr as of a late, and I've noticed some interesting things.

To start, I've just recently noticed that the overall delta V of a craft is heavily affected by engine weight, sometimes even to the point of affecting which engines I'd prefer to use. Previously, I'd picked engines solely based on their ISP, size relative to the craft/stage, and the overall twr of the final craft/stage. However, since 1.6 added the delta V display to the stock game, I've been gradually prioritizing it over those other things.

Nowadays, I'm often shocked to find that the Delta V shoots up when I use an engine with noticeably lower thrust and ISP, seemingly just because of how light the engine is comparatively. I've started using the Spark engine over the terrier in all my deep space 1.25m craft in my early science games, despite the size the difference being quite noticeable; the delta V will tend jump up by shocking amounts just by swapping into the lower efficiency engine! I've even run into some scenarios that make seemingly worthless engines worthwhile; despite the poodle appearing to be inferior to the wolfhound in a variety of ways, it actually gives the craft more delta V in many cases! I'm sure this is an obvious thing that rocket science has to take into account, and I probably look quite dumb to a lot of people right now, but I just find it fascinating how a difference in mass of 1.55 tons can make 113m/s of delta V come from a noticeably less efficient engine!

I was just wondering if there was a good way to quickly quantify this at a glance looking at the engine stats. As it stands, I'm only really able to find the best engine for a craft through trial and error, since I'm not really sure how the engines weight plays into things. I've gained a general intuition for how thrust and ISP factor into a crafts design, and this new variable is getting me all confused 

And now for the "Kerbal" aspect of things; I've recently been infatuated with the idea of making a rocket with the highest possible twr that can reasonably be achieved. I personally find it hilarious when I make rockets that are so powerful, that they are immediately burned up before they could ever hope to hit space  Does anyone have any tips for getting the most twr per part, while keeping burn time high enough to use that twr? I'd love that 

[Epicdreamer]

My thoughts about...

I think of twr when delt with celestial bodies. As long as twr is above 1 at the surface, I'm good to go.

I think of Dv to reach places. Farther away places need more Dv. Unless gravity assists, didn't really get the hang of multiple ones yet. I think of needing quite a lot more Dv to land on atmospheric bodies than twice the groundspeed on a low(est) orbit, compared to vacuum bodies. Think of clicking the speedometer to switch to (relative to) ground/orbital/target speed

I think of isp when traversing the Kerbol system. Higher isp in the same formfactor gives more Dv, mostly less thrust. So burns take longer.

I think of mass ass a value that influences all. Less mass means higher twr, so high isp/low thrust engines take less time to burn Dv. But mass consists mainly of fuel, which essentially is Dv. Aah the trade off...

But i do agree, the lightest engines can often give more overall efficienty, even with lower isp. I use the sparks mainly on lowG landers, but that's more because I dont like 10 min burns on high mass vessels with a low mass, less thrust engine.

I think of balancing those 4 values all the time when designing.

 

Best Kerbal rocket?

Ehm, depends on the purpose, but bottom up: a multistaged asparagus first stage, think of engines with (enough) gimbal, srb's for higher twr. Moar boosters!  Launching at 1.10-1.40 twr. As few high isp engines as possible for outside the atmosphere. And from there the payload, which depends on the mission at hand.

 

Edited May 15, 2019 by Epicdreamer
Grammatical correction

[OhioBob]

Which engine gives the most delta-v in a particular application often depends on how much delta-v you need.  Delta-v is a function of mass ratio and specific impulse.  Using a small engine is going to produce a higher mass ratio than using a large engine.  So even if the small engine has a lower ISP, in the right circumstances it can produce more delta-v.  But that's often the case only when you don't need a lot of delta-v and you're carrying a small fuel load.  When you need a lot of delta-v and are carrying a large fuel load, then ISP is likely more important.  A heavy engine in that case will reduce the mass ratio by only a small amount, and the higher efficiency will more than make up for it.

So when you're not burning much fuel, mass efficiency is most important.  And when you're burning a lot of fuel, fuel efficiency is most important.

[Zhetaan]

On 5/12/2019 at 11:08 PM, Pacca said:

I was just wondering if there was a good way to quickly quantify this at a glance looking at the engine stats. As it stands, I'm only really able to find the best engine for a craft through trial and error, since I'm not really sure how the engines weight plays into things. I've gained a general intuition for how thrust and ISP factor into a crafts design, and this new variable is getting me all confused 

Quickly?  No.  @OhioBob is accurate as usual, so I will give you what I can to help the calculation.

The Tsiolkovsky Rocket Equation is a function of two variables:  one is the mass ratio, and the other is the engine exhaust velocity (which is proportional to I_sp).  We can play with the equation a bit and see what it does in different circumstances:

dV = v_exh * ln (m_w / m_d)

Where v_exh is the exhaust velocity (equal to I_sp * 9.80665) and m_w / m_d is the mass ratio (equal to wet mass divided by dry mass).

The first thing to note is that mass ratio, though important, has a much-depressed effect on the overall value because of the natural logarithm.  The natural log of 10 is approximately 2.3, and the natural log of 100 is about 4.6.  The natural log of 1000 is about 6.9, and the natural log of 10,000 is about 9.2.  This is, mathematically, the reason why adding more fuel has diminishing returns:  the natural log only doubles with the square of the argument.  If you know your rules of logarithms, then you can see why that is:  ln x² = 2 ln x.

Natural log only changes rapidly with very small values, so mass ratio controls the equation only at very small values.  However, because the mass ratio is wet (or total) mass to dry mass, the mass ratio is constrained to values greater than or equal to one, which significantly limits its ability to help the delta-V situation.  Of course, a mass ratio of precisely one doesn't help, because the natural logarithm of one is zero.  This should make sense, because a mass ratio of one means that wet mass exactly equals dry mass--that is, there is no fuel.

That only covers one half of the equation, though.  What about exhaust velocity (I_sp)?

When comparing engines, you can see what you get from comparing the effects on the rocket equation.  For the most part, this reduces to a straightforward comparison of v_exh or I_sp values because that parameter is included unmodified in the equation, and for all but the smallest-mass rockets, the mass ratio is substantially similar.  For two engines of equal mass, v_exh or I_sp values  are the only point of comparison in the rocket equation.  By contrast, for two engines of equal efficiency, mass is the only point of comparison, but all that means to say is that you need a compelling reason to pick a heavier or less efficient engine (the usual reasons are thrust and ground clearance).

Mass of the rocket can give us the compelling reason if we look correctly:  Let's take two rocket equations, one for a Spark-powered rocket and one for a Terrier-powered rocket, and set them equal to one another.  The v_exh values for each engine are in the low to middle three thousands, but we can compare I_sp values directly in this case, because they divide out:

320 * ln (m_wSpark / m_dSpark) = 345 * ln (m_wTerrier / m_dTerrier)

Where m values are the masses of the rocket.  The Terrier is the heavier engine (by .4 tonnes), but we cannot simply subtract the difference in mass; the difference has to be figured into the ratio, like this:

320 * ln (m_wSpark / m_dSpark) = 345 * ln [(m_wSpark + .4) / (m_dSpark + .4)]

The variables in that equation are difficult to isolate, so in the spirit of laziness, let's not.  Instead, let's combine the I_sp values into a single ratio and, using the rules of logarithms, make that ratio into an exponent:

ln (m_wSpark / m_dSpark)^{(64 / 69)} = ln (m_wTerrier / m_dTerrier)

Since the logarithms are equal, so are the arguments:

(m_wSpark / m_dSpark)^{(64 / 69)} = m_wTerrier / m_dTerrier

How does this help us?  It gives a balance point:  the Spark is the less efficient engine, so the ratio of I_sp values is going to be less than one, which has the effect of reducing the value of that term.  However, the Spark is also the lighter engine, so all else being equal, it will have a higher mass ratio.  This equation tells us that if the mass ratio of the less efficient rocket is high enough, it can overcome the disadvantage of lower efficiency and still yield greater delta-V--you already knew that, obviously, but this is how to put it in figures.  Unfortunately, there is no way to give a specific answer for all rockets, because this comparison is dependent on the engine, the wet mass, and the dry mass:  in other words, if you take a light rocket that would normally give the Spark advantage but load it with lots of fuel, then the greater efficiency of the Terrier, given more fuel to work with, will shift the balance its way.  If you change the Terrier for a Nerv, then everything changes (though not so much as you might expect:  the Spark matches a heavier-but-more-efficient engine for very light rockets, so it largely matches the even-heavier-but-even-more-efficient engine in the same way).

Overall, here's a general equation that will apply to any rocket:

(m_w1 / m_d1)^{(I_sp1 / I_sp2)} = m_w2 / m_d2

You can find those values easily enough in the VAB.

On 5/12/2019 at 11:08 PM, Pacca said:

And now for the "Kerbal" aspect of things; I've recently been infatuated with the idea of making a rocket with the highest possible twr that can reasonably be achieved. I personally find it hilarious when I make rockets that are so powerful, that they are immediately burned up before they could ever hope to hit space  Does anyone have any tips for getting the most twr per part, while keeping burn time high enough to use that twr? I'd love that 

Reasonable?  I won't send you to see Whackjob, then.

This is actually very straightforward:  TWR, assuming launches from Kerbin's surface (the value becomes suspect when in orbit), is simply a function of thrust and mass.  Technically, it's thrust divided by weight, but if you're only considering launches from Kerbin's surface, then we don't need to consider gravity.  Given your objective, we also don't need to worry about ratios less than one.

Therefore, the best way to maximise thrust-to-weight is to reduce the mass of everything that isn't an engine to as near zero as possible, and use only the most powerful engines.  That implies Mammoths; they save a tonne over four Vectors and are the most powerful engines in the stock game.  That also implies an OKTO2 core, but if you don't mind the sacrifice, you can use a command seat and not need to worry about electricity.  As to burn time, I'm sure you know the answer--note that this is an occasion for decouplers, though perhaps not many.

Have fun!

[radonek]

On 5/13/2019 at 5:08 AM, Pacca said:

I was just wondering if there was a good way to quickly quantify this at a glance looking at the engine stats.

For me, simple rule of thumb is this:  how does weight of the engine compare with weight of rest of the payload (that is, everything that is not fuel)? Or put another way - if I add hypotetical fuel tanks to lighter engine to make up same total weight as the heavier engine, would I gain anything?

For (exaggerated) example, if I compare spark with LV-N, it means  _tons_  of fuel for spark. Now, if my craft is a small comm probe with something like small toroidal tank, those tons of extra fuel will obviously add a much more delta-v then what better efficiency of LV-N can save. On the other hand, if I were to make a big tanker based on  good 'ol large orange tank, few tons of extra fuel does not make that much of a difference.

Edited May 17, 2019 by radonek
mistake

[FleshJeb]

I wish someone would remake travert's optimal engine charts. Those things were amazingly educational. This still works, but it's 3 years out of date:

 

[Snark]

On 5/12/2019 at 8:08 PM, Pacca said:

I was just wondering if there was a good way to quickly quantify this at a glance looking at the engine stats. As it stands, I'm only really able to find the best engine for a craft through trial and error, since I'm not really sure how the engines weight plays into things. I've gained a general intuition for how thrust and ISP factor into a crafts design, and this new variable is getting me all confused 

Yeah, here's the thing to bear in mind:  Engines are dead weight.  The less mass you have on your ship, the better.  If you had two engines that were absolutely identical in all other respects except mass, naturally you'd always pick the lighter one.  It would be unambiguously better for all situations.

Also, your dV is directly proportional to your Isp.  That's hugely important, since the only other way to add dV to your ship besides "higher Isp engine" is to add more fuel mass, but then you're fighting the rocket equation because that's logarithmic.  So, again, if you had two engines that were absolutely identical in all other respects except Isp, then naturally you'd always pick the one with the higher Isp.  It would be unambiguously better for all situations.

However... KSP engines are deliberately designed so there are tradeoffs.  Engines that have better Isp also tend to be heavier.  So "which one gives more dV" depends on other things, such as ship mass.

Let's say you're planning an interplanetary transfer stage, which will be running in vacuum.  Let's say you're trying to pick between, say... <thinking of two radically different engines> the LV-N and the Spark.

Which one's better?

Well, in terms of fuel efficiency, obviously the LV-N wins, by a wide margine.  Its Isp is 800, compared with the Spark's 320.  So, each kilogram of fuel gives you 800/320 = 2.5 times the oomph if you pick the LV-N instead of the Spark.  So that's the better choice, right?

Well... not so fast.  Because the LV-N gets better fuel efficiency, sure... but it also tips the scales at a whopping three tons, compared to the Spark's paltry 130 kg.  That means if you pick the LV-N over the Spark, you're lugging along an extra 2.83 tons of dead weight, which will hurt your dV.

So... does the better fuel efficiency outweigh the extra mass, or not?  Answer:  Depends on how big the ship is.  I'll pick two deliberately extreme examples:

1. Big ship.  Let's say that the rest of your ship, other than the engine, has a mass of 1000 tons.  So, you can go with the LV-N for a ship mass of 1003 tons, or with the Spark for a mass of 1000.13 tons.  That's hardly any difference at all, is it?  Less than 1% of the mass of the ship.  So, the fact that you'd get 2.5x the fuel efficiency will far outweigh the fact that the ship is a third of one percent heavier.  Clear win for the LV-N.
2. Little ship.  Let's say that the rest of your ship, other than the engine, has a mass of 0.5 tons.  So, you can go with the LV-N for a ship mass of 3.5 tons, or with the Spark for a mass of 0.63 tons.  Now it's a completely different situation:  yes, the LV-N has 2.5x the fuel efficiency... but now your ship has got over 5x the mass.  So in this case, it's a clear win for the Spark.

Also, note that if you're talking about an ascent stage rather than something designed for orbital operations, then the question gets even messier, because then you have to care about TWR, too (i.e. how much thrust the engine has).  Note that in none of my above remarks do I mention thrust even once.  That's because thrust is irrelevant to dV; all that matters is Isp and your fuel ratio.  However, for an ascent vehicle that's launching from Kerbin's surface... it loses a lot of dV to gravity losses, and in general you want a higher thrust to offset those.  Higher TWR is better... but high-TWR engines also tend to have low Isp, so that's another tradeoff to juggle.

In the end, there's no one simple "rule".  If you're considering alternate options, you just need to run the numbers for each (either with a calculator or something, or just try building both ways in the VAB and see what the numbers say), and then pick the one you like.

[FleshJeb]

3 hours ago, Snark said:

if you pick the LV-N over the Spark, you're lugging along an extra 2.83 tons of dead weight, which will hurt your dV.

One of the things that helped me understand engine performance on a gut level was the inverse formulation: What can I do with 2.83 tons more fuel?

This works especially well when you're doing "bottom up" design with a known lifter. In that case, craft mass is a fixed maximum and the remaining variables are engine and tankage.