# ∆v

Okay so now we can talk about delta-v (∆v from now on because it looks cool) in a larger context. We can see from the last post that the thing that really matters in space travel is how much you can change your velocity before you run out of gas. And I’ve talked previously about orbital mechanics. Let’s tie these together. First a diagram I have lifted from a much more detailed article about the topic at Wikipedia:

This is a map of the solar system from Earth to Mars assuming you are travelling using orbital transfers — that is, you don’t care how long it takes and your plan is to burn just enough to enter the orbit of your target eventually. Exactly which way you point and how long you travel depends on many factors that are largely out of your control — at a given time with a given rocket you have essentially one choice.

The numbers on that map are not distances but rather costs in ∆v. And this is why ∆v is the critical resource both tactically and strategically in Diaspora Anabasis: it’s the only resource that matters for planning. Everything else is roughly fixed. Everything you might do to influence travel is going to boil down to changing your ∆v resource or cost.

So to get from the surface of the earth to Low Earth Orbit (LEO) you need to go 9.3 kilometers per second faster than when you started. Soak that in. Notice that almost every other transfer is somewhere between cheaper and vastly cheaper. This is why starting your trip on a planet is so incredibly expensive and why space and low-gravity-planetoid bases are essential to industrialized (and certainly private) space travel: this is an unnecessary expense that dominates everything.

If you have a space craft with 11km/s ∆v in resources, you can reach orbit and sit there. If you built the same ship in orbit, however, you could go to Mars with resources to spare. LEO is 2km away. Mars at its closest is 56,000,000km away. It’s 20 million times more efficient to travel with orbital transfers from Earth orbit than it is to orbit the Earth. When people talk about how hard it is to go to Mars and how we so handily went to the moon remember that: those Mercury and Gemini project orbits were actually the very hardest part of the whole endeavour. Everything after that is vastly simpler.

Now what if you don’t use orbital transfers? What if you want to spend less than 18 months to go to Mars? Well, you spend more ∆v. You can speed up any orbital transfer by burning harder at the start and burning again at the end to slow down. It changes the path of the transfer substantially — you’ll get there faster because you’re going faster but also because you’ll take a physically shorter path — your lazy elliptical arc will straighten as you dump reaction mass into the fire. But it costs twice as much because you have to slow down at the end.

You can think of an orbital transfer as basically matching courses with your destination (since planets are moving too). Imagine you want to catch up with a skier further down the slope than you. You can dig in the poles a little so you’re going faster and take an arcing path down the hill so that you slowly catch up, with friction equalizing your speed at intercept. It’s a lot of calculation and might need a little correction and it’s not the fastest path but it takes very little energy. That’s the orbital intercept.

Or you can drive on your snowmobile straight at your target. You’ll have to correct continuously as they move but you will arrive much sooner. You’ll also have to figure out how to slow down or you won’t be matching courses at all. That’s a “hyperbolic” intercept.

The other interesting thing on that map is the “aerobrake”. This is a way to steal ∆v from planets with an atmosphere: you can use that friction to slow down. We know that slowing down is just ∆v spent pointing backwards. So friction is free ∆v for slowing down! In the last post we talked about slingshotting, which steals ∆v from planets for speeding up. So the natural universe provides a landscape that can lighten the load and this is where strategic play will happen: we have a determination problem in that the math tightly constrains exactly how much ∆v a maneuver costs and you ship defines how much you have — so where are the player choices? What knobs can you turn to defy (rely manipulate) the math? The natural environment provides two.

We’ll talk about how the artificial environment can help next time.

# moving space ships

Let’s say we have a space ship and it’s moving at some velocity. It’s not accelerating — its drives are off — it’s just drifting. There is nothing to slow it down in space (no air resistance or other interesting friction sources) and nothing to speed it up. There’s no reason for it to change direction. It’s just going to keep going at this speed in this direction forever. For simplicity we’ll use units of meters per second and consider time in 1 second increments.

We can represent this situation like so:

On the right is our space ship and on the left is a vector indicating its velocity. In one second, the ship will be at the end of the arrow: its length indicates how far the ship will move in our 1 second tick. It’s predicting  the future for our space ship. This will go on forever.

Now if we want to turn, we can’t just steer — there’s no surface to get traction on, no wheels to redirect our momentum. The only tools we have are rotation and thrust. So that’s what we do. We rotate and we turn on the drive for a while, adding more velocity which we represent as a second vector in the direction of our burn. We can use the vector to find out where we’ll be next: we add a vector to the end of the existing one but at the angle of our burn.

So where will we be after our next tick? Well the trick with vectors is you add them nose to tail, preserving the angles, and then find the hypotenuse (sticking two vectors together gives you two sides of a triangle, and your new vector is the missing side of it!)

And we’ll see that with that little 40-odd degree turn and burn (adding velocity!) our new vector has us starting to turn to the left. But we are also going faster than before! And we’re not pointing in the direction we’re travelling. This, in my opinion, summarizes a great deal of what’s weird about travelling in space compared to a road vehicle — you can only add velocity, the direction you’re pointing in determines the direction of acceleration and nothing else, and you need to spend an awful lot of fuel to make an interesting change of direction. Let’s try that turn again but much more sharply.

We’re really cranking the wheel over here! The same rules for adding vectors apply of course so we get a final vector of:

Well that’s a tighter turn! Notice a few things. We’re totally pointing away from our direction of travel for one. For another, our vector is shorter: we’ve managed to slow down by adding velocity in a direction that partially opposes our initial vector. So now we know that the only way to slow down is the same as everything else in space travel: add velocity.

This is why in the latest rev of Diaspora we only track a space craft’s “delta-v” or its total ability to change its velocity. Everything about how it moves, how fast it moves, and where it goes depends on this value. It’s how you start, how you steer, and how you stop. And, when you’re out, you just follow that vector forever.

Well surely not forever. What if there’s a planet in the way? I’m glad you asked. Same rules.

So when you travel near another significant mass, it continuously adds a vector for you, whether you accelerate or not. So let’s say we’re passing by a planet. We have our existing vector but we also add a new one that points to the center of the mass and has a size (magnitude, we say) related to the total mass. Planets add pretty big vectors.

And the result is:

Wow! Notice a few things here. First, you don’t fall into the planet if you already have a big enough vector. If we had a smaller (or no) vector, we’d splat on the surface. But we fall past it! Precisely choosing altitude and vector is how we go into orbit: we just keep falling forever around the planet. But that’s not what this maneuver is going to do. The other thing to notice is that we are going way way faster than before — we’ve taken a ton of delta-v from the planet itself! Since delta-v is in such short supply, this has to be a useful move! We sometimes call it a slingshot maneuver, and it’s a very common way to get real spacecraft long distances in a relatively short period of time. Let’s look at the next second in this picture.

So now our two vectors are our original vector and the gravitational vector, which points to the center of mass of our planet:

Which gives us a result of:

We are going even faster now! All for free! And in a radically new direction.

Now, reality doesn’t actually progress in one second increments, so to find our actual path of travel we’d need to start looking at smaller increments. Do the vector addition every tenth of a second, every millionth of a second, refining and refining the path. This would be calculus, and we would see our actual path is a smooth curve. But the principle is the same and the result we care about is the same: we can steal velocity from planets.

In space all you can control is the change in your velocity, but you can steal velocity from planets. Another time we’ll talk about stealing negative velocity.

#### a note on gaming

This post is not about a game. You could game this way — it’s easy to see how you could do that, using counters or miniatures. It’s already been done too — Traveller, Triplanetary, Mayday, and even in 3-dimensional space in Vector-3. It’s not news for gaming. But my game targets people who don’t know the physics and maybe don’t care about it, but need a context to understand the design decisions that are based on physics. I will be leaning heavily into abstraction but you need to understand what you’re abstracting first.

# soft horizon style guide

Back when the VSCA was a business I thought I’d like to offer other writers the opportunity to make their own Soft Horizon games. New planes with their own themes that use the same rules, but interpreted through the lens of someone other than me. I really think the intrinsic diversity of Soft Horizon themes would be well served by a diversity of authors. Now, since I didn’t really take the business end seriously enough this never came to fruition (though it came close and there is at least one brilliant near-built plane out there).

Now that this isn’t a business I’d like to offer up the style guide. This was a kind of contract but of course that’s no longer necessary, so all the shalls should be read as shoulds. And I won’t publish or lay out or illustrate with you unless it seems like huge fun. If you do choose to make a Soft Horizon game and follow the spirit of the style guide here, we’ll have an anthology of wildly diverse but linked game, a psychedelia of shared space generators. And that would thrill me. I would love it if you at least POD produced it (which is damned near free to do — no risk at all) so I can have a shelf of books in this vein one day. And maybe I’d string them all together, with your permission, into a fat crazy book we can all wonder at.

# guide

Keep tone conversational and idiomatic: let your authorial voice out.

Provide illustration notes as comments in your submission in case we get around to finding an illustrator. Better yet, illustrate it yourself. Your artistic talent isn’t relevant.

You should recommend or produce at least five illustrations.

Use gender neutral pronouns or sentence structure unless the setting demands distinction.

Whenever considering sexuality, write in diversity.

Whenever considering gender, write in diversity.

Whenever considering “race”, write in diversity.

Whenever considering disability/ability, write in diversity.

Be political; don’t be shy. These planes can be metaphors. Should be.

If swearing moves your narrative along, swear like a motherfucker.

Write as much as you need to develop your idea: there is no word minimum nor maximum.

Providing a map may indicate that your text is too specific. Providing a way to create maps indicates that your text is supplying the table with tools to create rapidly and in context.

That is a general statement disguised as a specific one.

## INTRODUCTION

Write a custom introduction

## SYSTEM

Re-write SYSTEM section in your voice keeping the system materially identical but replacing examples with setting specific examples.

Do not change the METHODS list as characters need to be portable.

Do not change the RISKS list though absolutely change examples to mate with your setting.

Do not change how wounds and debt works unless the change is ADDITIVE (adds new options and does not change or delete old ones) and CONTEXTUAL (clearly adapts the material to the new setting).

Do not change how progression works unless the change is ADDITIVE and CONTEXTUAL
Do not change the ref’s role (especially the GM moves) unless the change is ADDITIVE and CONTEXTUAL.

Whatever you add to the system:

• The ref NEVER rolls in a resolution process
• There are NEVER flat modifiers (+1, +2, whatever) to the rolls

Be aware that failure and risk realization are an engine that makes this game easy to ref. If you reduce the failure rate too much the game will stall. And it has to survive progression as well.

## SETTING

Organize and explore your setting any way you like. It is not necessary to keep the organizational structure of the setting section in any other SH book.

Ensure that there are ways to develop places and people with a minimum of referee effort.

Lean on ORACLES, simple short text open to interpretation. Give the player something to create from rather than creating for them.

Sell your theme not you details. The players will bring the detail.

Ensure that the SETTING section ends with a note on the Soft Horizon and how your setting links to it.

## CHARACTERS

Re-write to suit your setting.

Try to keep to the power scale established in THE KING MACHINE but you do not need to be strict about it.

The DENIAL mechanism needs to be retained.

Ensure that you have developed a way to start the game with the player characters together and working towards a shared goal or mission.

Re-use the association rules if you like; modify as needed.

Find a novel element of your setting to bake into character creation. For KING MACHINE it’s simply that racial differences are real: different apes are distinct and visibly different species and have mechanically distinct features. This is only interesting if that’s not the case everywhere. It’s especially nice if it’s ONLY the case there. In SAND DOGS the distinction will be a sort of life path system a la Traveller. Find another way to alter character creation such that you get the same basic end result (number and type of dice to distribute) but get there another way, delivering some new feature to character background or play or both.

## RUNNING THE GAME

Re-write to suit your setting.

Keep the note on fronts and preparation but tune to you setting and voice.

Add any sections necessary to guide a ref in your setting (such as the “dealing with inconsistency” section in King Machine).

Modify the ref’s cheat sheet to meet your needs.

# stress

One of the core components of Diaspora Anabasis is stress. When you want to improve a rolled result, including helping someone else improve theirs, you take stress. But stress is not an inert hit points track you run out of. Stress is intended to minimally model, well, stress. This turns out to have pitfalls I hadn’t anticipated.

Your first point of stress leaves you agitated. It’s easy to get rid of. You work out, talk out your problems, take a vacation, and so on. All the things your friends tell you to do when you’re freaking out actually work because you’re not all that stressed. Being agitated doesn’t even warrant a FACT on your character sheet. No problems here.

Your second point of stress gives you a compulsion. You write this in as a FACT on your character sheet: this is a true thing about your character that you are expected to incorporate into play. Your character keeps coming back to the topic related to their stress, even when it’s not appropriate to the scene. You are worrying something over and your compulsion is a signal that you are in distress. Getting rid of it requires getting away from the thing causing you stress. That can be hard in a space ship a million miles from actual air.

Your third gives you bad judgement. Again embodied by a FACT, your character is now bad at making choices about or related to something. Maybe you are becoming too careful. Maybe too daring. But your choices relating to your FACT are not the best choices. They instead are focused on whatever you’re stressed about. Clearing this one requires that you make a substantive change to your situation. In our game the captain of the vessel gave up their captaincy. So it has to be a big change.

Your last step of stress is withdrawal and at this point all of the other characters should be worrying. You need professional help and the support of your allies to clear this.

What I didn’t anticipate is how much this impacts the players. It can actually be quite upsetting.

One reason, of course, is because someone is telling you how to change how to play your character. Players rightfully buck at this. It’s one thing to be asked to narrate a limp because your leg is broken, but for some reason (and I say that not to diminish it but to express that I don’t fully understand it) it is way harder to take on a real-seeming psychological change. I suspect this is because of the way the human brain handles pretending things: when you pretend an emotion, your brain probably simulates the emotion just by running the mechanisms that actually evoke the emotion with with a little simulation flag set so you don’t forget you’re pretending. Bottom line is that pretend pain doesn’t hurt but pretend emotions do, to an extent depending on the person, cause you to genuinely feel.

That up there is two reasons of course: we don’t like being told to play our pretend personalities differently, and feeling real bad feelings can really feel bad.

The other thing that gets in the way is that you are basically asked to play your character sub-optimally. You’re expected to deliberately make bad decisions. Since we’re playing a game, there is a desire to solve problems correctly and bask in the glory of victory. Deliberately failing is genuinely hard for a lot of people. I put myself in that camp.

When this last came up we talked it out and found a way forward that addressed as much of these as possible by making sure the player still felt like they had authority (but were handed some creative parameters) and agency and also that they wouldn’t be made to feel badly in a way that they didn’t want to feel bad. Talking it through was a big deal for me both to identify just how much of a minefield this thing is and also to resolve it or at least set us up for success in the next session.

Anyway here’s a draft of my rules text relating to this issue:

Stress can be very onerous on players. It asks you to play suboptimally and at the same time engage the game material in a way that is designed to emulate the real effects of stress on humans. At the extreme end of the track it asks you to act in ways that may upset yourself and others: your character will be withdrawn, upset, and making bad choices. Here are some ways to handle it. Please use these in addition to your preferred safety tools (X-Card, Script Change, and so on).

• Don’t do it. Skip the facts. The stress system is not as powerful this way, which would be the point of not using it. If it upsets you, just don’t use it. It’s not more important than your fun.
• Discuss it. When a character gets into the deep end of stress, take some time offline to discuss how to engage the new facts in ways that are not too upsetting. Part of what’s upsetting is that the rules are telling you how to play your character which most people are resistant to, but if you discuss how you want to play it, you can make it your own.
• Help the stressed. If everyone pulls together to help the stressed character it can relieve the difficulties that this brings. It also makes great scenes and clears the stress! Everyone wins.