If you took a zoomable flashlight and placed it in the fully zoomed out (flood) position, that is the beam profile I’m wanting to achieve.
Kramer also answered this pretty well, I’m going after the “large moon” effect he described.
And Litebringer also answered the question in an earlier post here with “It’d make a kick-ass flooder” and “a nice wide flood that’ll be buttery smooth and even”
If you look into the 3 production lights that I’ve been mentioning throughout this thread, (Klarus Mi1C, Sunwayman T26C or the yet-to-be-released Utorch S1 Mini) you’ll get a better picture of my idea for modding a Convoy S or Jaxman E2 with a fixed convex lens. Those 3 lights are built for the same result I hope to achieve, basically a beam like a zoomie that’s fixed in flood position. And yes I think it will be a sharper focus to create a more even, balanced flood beam.
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I guess what you’re saying is “why not just buy a BD04 instead?” 
Well, if I were to just buy a production light it would be a different light than the BD04 (read on below) For this build I don’t want a zoomie, I have several zoomies already, and will probably get a few more, in fact I’m becoming slightly obsessed with them… (my zoomie thread): Zooming Model List (2018 Updated) Tell us about your newest zoomie!
For this I want a “fixed” (non-zoom) set up for several reasons:
1. Shorter, more compact.
2. Better thermal transfer.
3. No moving body parts.
4. More water resistant.
5. Don’t need throw for this.
The 32mm head of the BD04 is way too big for what I’m going after. The final form of this light is going to be an 18350 sized “mini” with straight tube and magnet tail. I may also sometimes swap to an 18500 tube for even more battery capacity. The 18350/18500 tubes are readily available for the S2+ and Jax E2, and I already have several. I’m also planning to boost the output. The full size BD04 with it’s larger moveable zooming head and usb charging is totally out for this concept.
The closest production light I could buy would be the Sunwayman T26C, however it is not available in NW, is lacking in output, and does not have a magnetic tail, it’s also somewhat expensive. I was thinking of getting one and swapping out the emitter, boosting output and adding a tail magnet, that’s when I got the idea to look into building the light.
The only detriment to not actually modding the Sunwayman is my build will only be a few mm shorter with 18350, compared to the Sunwayman with 18650. One of the advantages however is that I can choose my UI with the various firmware options such as Biscotti, Crescendo, Dr. Jones etc etc. Of the 3 production lights I keep mentioning here, my light will have better output than all 3 and better battery capacity than the Klarus or Utorch.