This mechanic was discovered by me, and i did the math for the solutions.

Contents

## Guide to Speed Based Long Distance Travel Mechanic

### What It Is and How It Works

This is an alternative to the conventional, Phasing-based Long Distance Travel.

A recent change made to “Fly Upwards” and “Fly Downwards” (they work the same for this purpose) able to ignore all speed caps. The only Projectile that seems to both be able to surpass the cap, and behave consistently at those high speeds is Tentacle.

We can use those super-fast Tentacles to traverse any distance in a few frames and then release any payload at the point where it lands. The distance can be calculated with high precision, although the math is harder than for phasing builds (similar to wisps). This allows for some fast and precise, easy-to-build Long Distance Travel wands, that use fly upwards/downwards and a combination of other speed modifiers, instead of Phasing. They excel at very large distances in particular.

**The Example builds**

- Orange: NG parallel world travel, using Accel, ExplP and 54 FlyUps
- Purple: NG+ and Nightmare parallel world travel, using 2Decel+40FlyUps
- Blue: compact entity duping (no specific distance, just far enough)

### Advantages

While it is significantly harder to find accurate solutions for this build, i am convinced that this is the only downside to this method, compared to the phasing-builds.

This method has certain advantages over the phasing method:

- It is faster.
- It causes basically no lag.
- It is at least as reliable.
- The builds are comparable in terms of the rarity of required resources, and for some configurations even cheaper than phasing builds.
- It requires no Alternate Component Lifetime like copy trail or All Seeing Eye, or knowing the timer length.

You can go absolutely insane distances, far beyond the engines capabilities, while remaining instant, lag-friendly and within 10-20 wand slots.

### Resolving Common Issues

- Notably, the wands’ hidden Speed Stat does not influence these builds, due to the Delayed Spellcast/Blackhole in front.
- All other Speed modifiers have to be applied before Fly Up/Downwads, since those cap the speed multiplier.
- Recoil can mess with Homebringer hitting you. add recoil dampener or press your back against a wall to avoid the issue, or use a swapper payload instead.
- Repulsion field messes with the build in two ways, but both can be overcome. It can influence the direction, which is resolved, by adding Long Distance Cast at the start (or similar).
- Repulsion field also makes it harder to hit yourself with homebringer. Either add a lot of boomerang or a vaccuum field to overcome this, or use a swapper payload instead.
- Deer swapper does not work, use fish instead.
- Swapper payloads can work with timers instead of Expiration triggers, but you need to reduce Tentacle’s Lifetime (1 Reduce is enough).
- Faster Projectiles requires furhter calculations. Check the comments for some solutions. They might not even need FlyUp.
- The modifier numbers have to be exact! Being just one off on any of the speed modifiers will teleport you somehere eintirely different instead.

**Details on how it works**

- The Expiration Trigger at the start serves two purposes: Neutralize the wands’ speed stat, and give linear arc a chance to act.
- InnerSpell+Homebringer is often used for convenience, since the usual LDT-Payloads are 4+ slots.
- Tentacle w timer has the quirk of releasing its payload at 0 speed, so no further modification of the homebringer is needed to hit the player.
- The entire distance is covered in a single 1-frame jump. after that the engine steps in and slows down the projectile to a halt (This is the current theory).

### Possible Replacements

- Either Spell Tentacle or Tentacle Timer are required.
- Either Fly Upwards or Fly Downwards are required (you can use Perks instead).
- InnerSpell+Homebringer can be replaced by a Swapper Payload, but you require entity fish_evakas and spell add death trigger on the tentacle, instead of a timer.
- Spell Tentacle Timer can be replaced with spell add timer + spell tentacle.
- Entity fish_evakas can be replaced by Spell summon deercoy, but requires additional modification.
- Nolla is optional, it just speeds things up.
- Linear Arc can be replaced by Horizontal Path for horizontal travel.
- DS/ “BH w DeathTrigger” can be replaced with WarpCast, or spell add death trigger on any Projectile unaffected by gravity (notably, timers dont work).
- Inner Spell can be replaced by True orbit, and using Vaccum Field to ensure the hit.
- Spell accelerating shot and Spell explosive projectile can be replaced with other speed modifiers, if the numbers are adjusted correctly.

**Finding your own solutions**

- Divide the distance (in pixels) by Tentacle’s base speed (~7.92 is currently the most accurate estimate).
- Using Speed Modifiers, try to get the cast state value “speed_multiplier” as close as possible to this value (This is hard).

*For reference:* For a NG PW jump we need ~4525 speed_multiplier, the example build is ~4528 (0.09% error), which is impressively accurate for the simplicity of the builds.

Note, that all other speed modifiers Cap the speed between 0 and 20, every increase past that has to come from Fly Up/Downwards, and you can not arbitrarily slow it down before applying FlyUp.

**More technical details about finding solutions (beware: maths)**

*I use the following notation*

- Distance: d
- Base-Speed: v(=7.92)
- Speed Modifier: m_i (say for example, m_0=1.2 is FlyUp, m_1=0.3 could be heavyShot …)
- Modifier Amounts: n_i (n_0 is the amount of FlyUps for example)`

To find Modifier-Combinations that come close to the required speed_multiplier, we need to approximately solve:

`d/v = Product(m_i^n_i)`

I looked for those solutions by a somewhat “clever” brute force search, starting from different values for n_0 (the amount of FlyUps).

I was able to re-use the wisp-calculator i wrote a while ago for this, by taking the logarithm of the equation and solving the linear counterpart:

`log(d/v) = Sum(n_i*log(m_i))``

Which has the same structure as the wisp equation (just not being limited to integer coefficients)

Attached are some hand-picked examples for different modifiers, and commonly required Distances, that are easy to build.

*Note: *“Complexity” is a somewhat arbitrary measure i use to sort solutions by “easiness-to-build”. the true most compact version we found is at the bottom of the list, don’t give it too much thought.

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