This guide will cover a specific usecase of cowl in regards to gaining speed. For that, I will go over some physics and the base mechanics of landing and converting velocity so this guide might be useful for general applications.
Fel's "A Trans Girl's Guide to The Sage's Cowl" is a great source for a more general look at how to use cowl. This guide will instead focus on the technical aspect of using it to gain speed, and might not be as useful for a beginner.
This guide was made after the april 3rd rebalance, and I have no idea how cowl was back then. This is meant for current version cowl as of patch 1.2.d.

At the end of the day (ignoring theming and plot), games are made of values, and functions (or "rules" if we're to go beyond computer games).

Zoe's speed, specifically horizontal speed towards the portal, is the main value we need to optimize in Haste. Speed generally follows standard ball-collider computer physics (duh), and so we have to deal with lotsa vector math~. Vector math is out of the scope of this guide but still, here's some vector stuff that is important:


As you can see, if we decompose Zoe's velocity by the Y axis, we have that green vertical velocity vector that we don't really care about, because it doesn't get us closer to the goal. The combination of activating cowl or fastfall lets us manipulate it quite freely.

Zoe's acceleration (ignoring boost speed and base ground movement) works by what we in Brazil would call "pegando embalo na descida", or in technical terms: converting gravitational potential energy into kinetic energy, and using a slope to redirect all that velocity forward. Zoe gains speed by this method exactly because she has extra supernatural forces to call upon, mainly fastfalling, so she isn't bound by the conservation of energy.


Zoe is very inelastic, which means velocity perpendicular to the landing angle gets lost in collision. In fact, all landings except [bad] landings result in her "sticking it" and not bouncing. That's why it's so important to get [perfect] landings, regardless of energy gain.

With that out of the way, let's see how you actually go fast.

Without the board or the hourglass, we can't straight up gain horizontal speed. We need to instead abuse fast falling to multiply our gravitational energy, gain lots of bonus downwards velocity and convert it to good speed, by landing with as little energy loss as possible and then using the ground (or a grapple) to redirect Zoe forward.



So. You have a value, [speed], and you need to keep it as high as possible for the duration of the level so you get to the end faster. Whenever you go up, you're spending speed to gain height and so potential [bonus speed] from fast falling. Whenever you fastfall into a slope, you're converting some of that [bonus speed] into horizontal speed and taking it with you for your next jump. Low ramps give you a lower flight trajectory, meaning you cash out more of your height to gain more [speed].



All of this makes you really not want to jump high, unless you are actively setting up for a big speed conversion. When you have enough speed, let's say ~150m/s when hitting the ground, you want to keep most of that speed towards the finish line.

So how does cowl break the speed economy?

Cawl gives you a vertical boost. Most people are already using it for gaining lots of height from ramps by stacking it on top of a jump, and also for course correcting to get good conversions and that sweet [perfect] landing. But there's a better, more abusable use for it. Interrupting your velocity conversion to gain more speed.


As the cheap item it is, using it to both gain height for a conversion, and then exiting that conversion early to get more speed is very easy energy-wise. It's not even that hard to use it once to get a high jump, once to correct your landing (though it loses speed), and then once to skip a ramp.


That small ramp there spends 10 whole speeds to give you a jump.
If you don't need that jump, spend energy instead! Keep your speeds working, people.