Engineering101

Delta V question

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So, I looked up delta V and apparently its basically synonymous with acceleration.

So what is all the fuss with Delta V readouts etc? Why are Delta V readouts necessary?

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In space there's no friction. That means it doesn't cost you anything to maintain your speed. That also means it does cost you energy to slow down. DV is how much speeding up/slowing down you can do for maneuvering.

Consider DV a measure for "how many miles you have in the tank." For instance, it will take you between 3,000 and 3,500 m/s DV to get into Kerbin low orbit (depending on how efficient your launch is). It will take roughly an additional 800 m/s to get a Mun encounter, and another, say, 400 m/s to turn that encounter into an orbit. If you want to return from that orbit to Kerbin it'll take another 200 m/s. So in total you'll need about 5,000 m/s DV to launch, orbit the Mun, and return. DV read-outs will tell you in advance if you're going to complete your mission, or run out of propellant along the way (assuming you don't waste any of it).

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The orbit you're in depends on where you are currently plus how fast you're going in what direction. To go places, you need to go from one orbit to another at the right point, and so on. To do that, you need to use your engines to thrust the right amount in the right direction. Delta V is a measure of how much your ship's engines can thrust. So delta V is important because it tells you what missions your craft can and can't do.

Borrowing one of Kerbart's examples for a moment, if you're in a low orbit around Kerbin, you have to be going at least 2250 m/s just to avoid falling into the atmosphere, simply due to Kerbin's size and mass, so you need to expend at least that much delta V to launch into such an orbit. But you also have to get up above the atmosphere in the first place, as well as push through the atmosphere. Adding those things together gives the 3000-3500 range he mentioned.

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1 hour ago, Engineering101 said:

So, I looked up delta V and apparently its basically synonymous with acceleration...

Not exactly. Acceleration is the instantaneous change in velocity of your vessel; the second derivative of position with respect to time:

a = dV/dt.

Detla-V, on the other hand, is a measure of either: (1) the vector difference between two velocity vectors through a point, describing a maneuver to move from one orbit to the other, or (2) the maximum magnitude of such a vector difference that a vessel can achieve.

dV = dV.

Yes, it's the same dV as in the acceleration equation above. So it's a part of the acceleration. Strictly speaking, though, when we deal with dV we assume a maneuver of zero time. We're describing the result of a change in velocity; not the time evolution of the change itself.

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Delta means change, and V means velocity, so it literally means "change in velocity"

No matter how big or small your spacecraft is, it will always take the same X amount of delta-v to go from A to B.  (assuming the mission profile is executed the same)

However, a big heavy craft will require much more fuel to make the same change in velocity than a small light craft, and different engines can use that fuel more or less efficiently than others.

Edited by Brofessional
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Just to mention, it is called delta-V for the greek letter delta (looks like a triangle), which in mathematics is used to denote a change in value.

So delta-V is just initial velocity minus final velocity.

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11 hours ago, Engineering101 said:

So what is all the fuss with Delta V readouts etc? Why are Delta V readouts necessary?

Δv readouts come with some mods such as KER or MechJeb.  What the readout does is it tells you the amount of Δv your rocket/spacecraft is capable of producing.  You need to make sure that your vehicle can produce at least as much Δv as it will take to complete the mission you plan to fly.  Determining the amount of Δv you need is generally done using a Δv map, such as this one.

Let's say you want to orbit Mun and return.  According to the Δv map, this should take 3400+860+310+310 = 4880 m/s.  If you build a vehicle in the VAB and your KER readout says it can produce 4500 m/s, then you don't have enough to complete the mission you want to fly.  You have to start redesigning you vehicle until the readout gets up to at least 4880 m/s (and preferably a bit more to give you a safety margin).  If you get your readout up to, say, 5000 m/s, then you should have a vehicle capable of orbiting Mun.

Of course you also have to learn to fly efficiently.  If you do things poorly, you can waste a lot of Δv.  If you are doing something for the first time and are not entirely sure how it will go, you should probably carry a large margin to play it safe.

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12 hours ago, Brofessional said:

Delta means change, and V means velocity, so it literally means "change in velocity"

No matter how big or small your spacecraft is, it will always take the same X amount of delta-v to go from A to B.  (assuming the mission profile is executed the same)

However, a big heavy craft will require much more fuel to make the same change in velocity than a small light craft, and different engines can use that fuel more or less efficiently than others.

@Engineering101, this is the crux of why dV is "all the fus" if you're looking for the most plain-english answer.  dV in real rocketry became the norm exactly because it describes the maneuver, without any of the variables that would be specific to a given craft - it's mass and engine efficiency.  It's a common launguage.

Let's say Starship A is a huge ship.  It launches Shuttle B.  They are both in the same orbit and going to the same place today.  Shuttle B starts with a full tank and performs a course correction, and then reports to Starship A that they have used 5 liters of their fuel.  But if Starship A expends only 5 liters, its course is barely shifted at all.  

If instead Shuttle B tells Starship A their change in velocity was 400 meters per second (distance divided by time is acceleration) then Starship A can calculate they need to use more like 1000 liters of fuel to achieve that 400 m/s change in velocity.  If Shuttle B also gives them a vector (the direction they pointed) then Starship A can perform the same maneuver precisely.

Fun fact: since we said their engines are identically efficient, then if the shuttle were parked in the starship, the maneuver would have cost the starship 1005 liters - the starship's expendature plus the shuttle's expendature.

 

Edited by Kyrt Malthorn
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dV=range

(A tad over-simplified but good enough to get started with). 

Edited by Foxster

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31 minutes ago, Foxster said:

dV=range

(A tad over-simplified but good enough to get started with). 

Except that's wrong in literally every particular....

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1 hour ago, PanzerAce said:

Except that's wrong in literally every particular....

Except it isn't.

If you are starting out in KSP and want to know what measure you need to change to increase a craft's range from reaching the Mun to reaching Duna then it is dV.  

Sure, you can wrap dV in some maths or technical description but how is that going to help someone starting out in KSP?

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One thing nobody has seemed to mention so far is:  since your rocket gets lighter as you burn its fuel -- the real deltaV of your rocket is always a bit more than what the instantaneous readouts tell you.

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16 minutes ago, bewing said:

One thing nobody has seemed to mention so far is:  since your rocket gets lighter as you burn its fuel -- the real deltaV of your rocket is always a bit more than what the instantaneous readouts tell you.

Uh, no, the Tsiolkovsky rocket equation is taking that into account.  If it did not, they would be HORRIBLY wrong.  That's why it has a natural logarithm with a mass ratio stuck in the middle - that's the calculation.

The calculation is correct.  It's the maneuver nodes which are somewhat optimistic about a typical craft acceleration (wildly optimistic when ions are involved).

NB: One does not require a read-out to calculate delta-v.  The Tsiolkovsky rocket equation is rather trivial to enter into a calculator - just pre-multiply the specific impulse in seconds with 9.80665 (9.8 for laziness, but I never want to see any scripts or programs that aren't 9.80665), and then multiply that by the current mass divided by dry mass (for an LF/OX rocket, every 90 units of fuel is 1t with it's accompanying 110 oxidizer).  That can be updated at will when the current (or wet) mass changes.

Example:

5t ship with 180 fuel = 5t wet, 5t - (180 fuel / 90 fuel/ton=2 tons of fuel) 2 = 3t dry.   Say the ship has a 909, which gives it 345 specific impulse, and thus (345*9.80665) ~ 3,383.3 exhaust velocity.   3,383.3 * ln(5/3) =~ 1728.3 delta-v.

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14 hours ago, Renegrade said:

One does not require a read-out to calculate delta-v.  The Tsiolkovsky rocket equation is rather trivial to enter into a calculator - just pre-multiply the specific impulse in seconds with 9.80665 (9.8 for laziness, but I never want to see any scripts or programs that aren't 9.80665), and then multiply that by the current mass divided by dry mass (for an LF/OX rocket, every 90 units of fuel is 1t with it's accompanying 110 oxidizer).  That can be updated at will when the current (or wet) mass changes.

Solving the Tsiolkovsky rocket is the easy part, getting the numbers to enter into the Tsiolkovsky rocket equation is the hard part.  The VAB tool that comes with the stock game provides the total vehicle mass only.  It doesn't break it down by stage and it doesn't give the propellant mass.  To get the stage breakdown we have to start disassembling the rocket stage by stage and note how much the mass changes.  The mass is also given only to the nearest 0.1-ton, which many times isn't precise enough.  And the propellant mass must be added up by hand from the contents of each fuel tank.  In other words, it's a real pain in the neck to do it without using something like KER.  KER not only computes the dV, but it also adds up all the bits and pieces that goes into the calculation.  It's the latter part that is the biggest convenience and time saver.

 

Edited by OhioBob
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On 3/27/2016 at 2:49 PM, Kerbart said:

In space there's no friction. That means it doesn't cost you anything to maintain your speed. That also means it does cost you energy to slow down. DV is how much speeding up/slowing down you can do for maneuvering.

Consider DV a measure for "how many miles you have in the tank." For instance, it will take you between 3,000 and 3,500 m/s DV to get into Kerbin low orbit (depending on how efficient your launch is). It will take roughly an additional 800 m/s to get a Mun encounter, and another, say, 400 m/s to turn that encounter into an orbit. If you want to return from that orbit to Kerbin it'll take another 200 m/s. So in total you'll need about 5,000 m/s DV to launch, orbit the Mun, and return. DV read-outs will tell you in advance if you're going to complete your mission, or run out of propellant along the way (assuming you don't waste any of it).

Riiiight I get it now. Yup, I can see why that would be very useful.

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On 2016-03-26 at 6:41 AM, Engineering101 said:

So, I looked up delta V and apparently its basically synonymous with acceleration.

So what is all the fuss with Delta V readouts etc? Why are Delta V readouts necessary?

Delta-v means velocity change. And the way you change your velocity is by applying acceleration so yeah, they're pretty much the same thing.

Knowing how much dV it takes to get somewhere is like a golfer knowing how hard he needs to hit the ball to reach the hole (how much acceleration he needs to apply to the ball).

A dV readout like Mechjeb or Kerbal Engineer will basically tell you your golf ball hitting budget.

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On 28.3.2016 at 4:20 AM, OhioBob said:

Solving the Tsiolkovsky rocket is the easy part, getting the numbers to enter into the Tsiolkovsky rocket equation is the hard part.  The VAB tool that comes with the stock game provides the total vehicle mass only.  It doesn't break it down by stage and it doesn't give the propellant mass.  To get the stage breakdown we have to start disassembling the rocket stage by stage and note how much the mass changes.  The mass is also given only to the nearest 0.1-ton, which many times isn't precise enough.  And the propellant mass must be added up by hand from the contents of each fuel tank.  In other words, it's a real pain in the neck to do it without using something like KER.  KER not only computes the dV, but it also adds up all the bits and pieces that goes into the calculation.  It's the later part that is the biggest convenience and time saver.

 

You can just right click the tanks of the stage in question and remove the fuel to get the dry mass of said stage. Still, that's rather inconvenient and gets annoying as soon as you deal with a bigger multi-stage craft. Also, it's pretty easy to forget to refill a tank before launch...

And no, Delta-v and acceleration are two very different beasts. Delta-v is what you get when you accelerate for a certain time, or mathematically written: gif.latex?\Delta&space;v&space;=&space;\, where a(t) is acceleration at time t, t0 is the time when you start to accelerate, and t1 denotes the end of acceleration. For a constant acceleration a=const, this formula simplifies to gif.latex?\Delta&space;v&space;=&space;a.

And since nobody cared to write the Rocket equation down yet, here it is, in all its gory glory:

gif.latex?\frac{m_\mathrm{wet}}{m_\mathr

Or rewritten, to give Delta-v:

gif.latex?\Delta&space;v&space;=&space;g

The derivation is actually pretty straightforward, and follows directly from the conservation of (linear) momentum. During the burn, the rocket expels mass at a given rate, and at a given exhaust velocity. Observed from an inertial frame of reference (a frame of reference that itself isn't subject to any acceleration - this makes calculations a lot easier, as accelerated frames of reference would require us to take into account fictitious forces), the momentum carried away by this expelled material is given by

gif.latex?\frac{\mathrm{d}p}{\mathrm{d}t

where vrocket is the rocket's velocity at time t, vexhaust is the velocity relative to the rocket at which the propellant is expelled (assumed to be constant), and dm/dt is the mass flow rate (in mass units per time, for instance in kg/s if one is using the international system).

This means that the rocket's momentum has to change by the same amount:

gif.latex?\frac{\mathrm{d}m_\mathrm{rock

Now using the product rule of calculus, we get:

gif.latex?v_\mathrm{rocket}(t)\frac{\mat

Of course the change of mass of the rocket is just the negative value of the mass flow:

gif.latex?\frac{\mathrm{d}m_\mathrm{rock

This gives:

gif.latex?0=v_\mathrm{rocket}(t)\frac{\m

what can be factorized to yield

gif.latex?\frac{\frac{\mathrm{d}v_\mathr

This can now easily be integrated, as on the left hand side we just have the rate of change of v(t) divided by a constant, and on the right hand side we have the rate of change of m(t) divided by m(t), what is, as one learns in basic calculus, just the rate of change of ln(m(t)).

gif.latex?\int\limits_{t_1}^{t_2}\frac{\

gif.latex?\frac{v%28t_2%29-v%28t_1%29}{v

What is now missing to get the form of the Rocket Equation given above, is that the specific impulse is just a way to measure exhaust velocity in a unit that is part of both, the international unit system (as used by NASA) and the old unit system (used by some of NASA's component suppliers). It's related to the exhaust velocity simply by gif.latex?v_\mathrm{exhaust}&space;=&spa, where g is the gravitational acceleration at sea level of earth (measured in whatever fancy units one uses).

 

Edit: On the use of Delta-v in spaceflight:

One cool thing about gravity is that it's proportional to mass (F=G*M*m/r²), the same mass that's responsible for inertia. This means that in Newton's equation of motion (F=m*a) the mass of the craft cancels out. A consequence of this is, that no matter how your craft looks like and how heavy it is, if it has a certain velocity and position (both as vectors, meaning magnitude + direction) within a gravitational field, its path is defined. Therefore, the flight path of a craft can be perfectly reproduced with any other craft by changing the velocity in exactly the same manner (magnitude+direction) at exactly the same points. So, when planning a mission, one first sums up (the magnitude of) all velocity changes (Delta-v) required for the trip. Once one knows this sum and has the desired payload, one can start dimensioning the required fuel tanks using the Rocket Equation.

As Delta-v is such a useful quantity, certain diagrams, known as Delta-v subway maps, have been drawn:

Delta-V map for the Kerbin System

Delta-V map for the real solar system

The values for transfers between planets/moons are more or less exact, the values for landing/launching are based on experience, as the actual numbers depend on your craft design (TWR on non-atomspheric bodies, while on bodies with an atmosphere atmospheric drag will also play a role).
It's also not too hard to calculate those numbers yourself. The transfers themselves are calculated as Hohmann transfers, and one also has to take into account Oberth Effect.

Edit 2:
I just realized that the terms of use of the service I'm using to render the equations require a link back, so, if anyone else would like to write LaTeX equations online, have a look at their website: http://www.codecogs.com

Edited by soulsource
Added link to LaTeX equation renderer.

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On 26-3-2016 at 6:41 AM, Engineering101 said:

So, I looked up delta V and apparently its basically synonymous with acceleration.

Where you can get to in space is largely a matter of how much velocity your ship can make, also known as delta-v.

But the d-v number does not tell you how long it takes to reach that velocity, so it is not equivalent to acceleration. Two ships can have the same d-v but different acceleration, and vice versa.

Equivalent to acceleration is thrust-to-weight ratio (TWR).  

 

Edited by rkman

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The easy way I remember it:

Delta-V is the amount of velocity change.

TWR (and acceleration) is the rate of velocity change.

(A bit of an oversimplification, but helpful for understanding the concepts.)

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13 hours ago, OhioBob said:

Solving the Tsiolkovsky rocket is the easy part, getting the numbers to enter into the Tsiolkovsky rocket equation is the hard part.  The VAB tool that comes with the stock game provides the total vehicle mass only.  It doesn't break it down by stage and it doesn't give the propellant mass.  To get the stage breakdown we have to start disassembling the rocket stage by stage and note how much the mass changes.  The mass is also given only to the nearest 0.1-ton, which many times isn't precise enough.  And the propellant mass must be added up by hand from the contents of each fuel tank.  In other words, it's a real pain in the neck to do it without using something like KER.  KER not only computes the dV, but it also adds up all the bits and pieces that goes into the calculation.  It's the latter part that is the biggest convenience and time saver.

 

That's true, but it's not that hard to add up the propellant masses - the tanks are doubling in a binary fashion until you get into the NASA parts.  In upper stages, it's quite easy.  When you get to the lower stages, it does get to be a bit of a pain, but that can be amortized by re-using those launch stages.  Improvements to the subassembly system makes this a lot easier.  I played this way at first for a long time until I understood the way the equation worked, and it wasn't particularly onerous.

Note also that when I started, there was no mass indicator in the VAB at all, but it was quite easy to launch to launchpad, take notes there, and recover the vehicle.  The indicator in flight (map->craft info) is significantly more accurate.    That's not really necessary though, as one can simply add 0.1 to the mass of the craft and over-engineer slightly.  Note that my example craft above with a .1 added to it goes from 1728 to 1684 - a three percent difference.

That being said, I wouldn't mind a more accurate readout that also gave wet/dry mass per stage..might actually be workable post-1.1 as I understand staging has been re-written (it was a Charlie Foxtrot in the past, which can confuse said mods at times).

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2 hours ago, soulsource said:

What is now missing to get the form of the Rocket Equation given above, is that the specific impulse is just a way to measure exhaust velocity in a unit that is part of both, the international unit system (as used by NASA) and the old unit system (used by some of NASA's component suppliers). It's related to the exhaust velocity simply by gif.latex?v_\mathrm{exhaust}&space;=&spa, where g is the gravitational acceleration at sea level of earth (measured in whatever fancy units one uses).

Actually, it's g0, or standard gravity, which is a defined number that may or may not be like gravity at sea level, depending on where you are.  It won't make a big difference in hand calculations, but the correct value for any programs, scripts, or spreadsheets is 9.80665 (in metric/SI units - meters/sec^2).  KSP used to use 9.82 for some boneheaded reason, but that was corrected back in 0.90 or earlier.

Edited by Renegrade

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I found the easiest way to find the mass ratio in the VAB, without tools, was to note the mass and then remove all fuel from the tanks and note the mass again.  Fairly easy to do if you keep the number of individual tanks to a minimum, something KSP is bad at in general.  In the toy solar system it's not critical to get the calculations exact since everything requires less and all the tanks are Lego-like constructs.  In RO/RSS, using procedural tanks, I don't play without aids.

Edited by regex

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5 minutes ago, Renegrade said:

That's true, but it's not that hard to add up the propellant masses - the tanks are doubling in a binary fashion until you get into the NASA parts.  In upper stages, it's quite easy.  When you get to the lower stages, it does get to be a bit of a pain, but that can be amortized by re-using those launch stages.  Improvements to the subassembly system makes this a lot easier.  I played this way at first for a long time until I understood the way the equation worked, and it wasn't particularly onerous.

Note also that when I started, there was no mass indicator in the VAB at all, but it was quite easy to launch to launchpad, take notes there, and recover the vehicle.  The indicator in flight (map->craft info) is significantly more accurate.    That's not really necessary though, as one can simply add 0.1 to the mass of the craft and over-engineer slightly.  Note that my example craft above with a .1 added to it goes from 1728 to 1684 - a three percent difference.

That being said, I wouldn't mind a more accurate readout that also gave wet/dry mass per stage..might actually be workable post-1.1 as I understand staging has been re-written (it was a Charlie Foxtrot in the past, which can confuse said mods at times).

I agree that it is not exceedingly difficult to get the information, but it is certainly inconvenient.  And getting the information to plug into the equation is by far the more time consuming part of the process than is solving the equation, which was my point.

Like you, I started using the mass indicator in the map view.  I'd send my rocket out to the pad, switch to map view, note the mass, and then revert to the VAB.  Then strip away the first stage, and do it again to get the starting mass for the second stage.  Ditto again if there was a third stage, and so on.  Then I'd have to add up the propellant mass for each stage.  There is nothing especially difficult about all that, but it takes time and it's sure not what I consider to be fun.  And we haven't even mention the situation were we have a liquid core with strap-on SRBs.  First we have to compute the combined Isp, then we have to compute how much liquid propellant is remaining after the SRBs are jettisoned.  I did all of that for months before I finally surrendered and said screw it and installed KER.

I think it is a really good exercise for somebody to figure out how to do all of that.  I'm all for learning.  But once somebody learns it, it seems rather pointless to have to go through the grind time after time.  I love math, but for even me having to do all that detracted from the enjoyment of the game.

 

 

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1 minute ago, OhioBob said:

I think it is a really good exercise for somebody to figure out how to do all of that.  I'm all for learning.  But once somebody learns it, it seems rather pointless to have to go through the grind time after time.  I love math, but for even me having to do all that detracted from the enjoyment of the game.

Yeah, once you've learned it and .. well, grok it, there's no need to keep on doing it.  My main points where A) it's possible and not too onerous to do it, and B) it's a good learning experience.  Well, and once you know it, it can help when your utility of choice doesn't understand a rapier in LF/OX mode or isn't available in the current version (Hello 1.1 bug squishing party!) etc.

I started doing it by hand, then I moved to scripts I wrote, then I used KER, then KER+VOID, and now just VOID with the occasional assistance from my script or quick calculation by hand if VOID gets confused or I'm trying to do something weird like calculate remaining RCS delta-v... (the script has built-in constants for LF/OX from either an LF or OX readout, monoprop, solid fuel, xenon, and even Karbonite for some reason heh) 

BTW, VOID might not be as capable, but it's HUDs are much more compact and are less uh.. intrusive than KER's...

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15 hours ago, Renegrade said:

NB: One does not require a read-out to calculate delta-v.  The Tsiolkovsky rocket equation is rather trivial to enter into a calculator - just pre-multiply the specific impulse in seconds with 9.80665 (9.8 for laziness, but I never want to see any scripts or programs that aren't 9.80665), and then multiply that by the current mass divided by dry mass (for an LF/OX rocket, every 90 units of fuel is 1t with it's accompanying 110 oxidizer).  That can be updated at will when the current (or wet) mass changes.

Calculating the delta-v for simple craft is trivial.  Strap on some SRBs (while the main [liquid] rocket is also firing and you will either need to download KER or dig into the derivation to figure out where to plug in all the changes).  Note that the equation will naively insist on using low-Isp fuels first, without any checking on the efficiency changes due to the TWR changes.  This is pretty critical to understanding where delta-v fits in importance.  It is more or less everything between bodies (assuming you are willing to perform Mangalyaan maneuvers to get there) but you must balance TWR for take-off and (powered) landings.

Once you understand delta-v, get a load of this:

600px-KerbinDeltaVMap.png

Pretty much a complete guide to the Kerbol system.  Just remember ULA's recent launch and have a good sized fuel margin.

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