Spent two weeks designing my own rocket on paper, finally got the math to work out

I was in the same spot at 12, filling a school notebook with designs I couldn't build yet. What acutally got me flying sooner was asking my dad to drive me to a local club launch. Turns out you don't need your own motors or money for most of it. A guy there let me prep my own Estes Alpha under his range box, and by the end of that summer I'd flown a Blob I built myself with a B6-4. Nobody cared that I was a kid, they just cared that my nose cone fit.

The design work you're doing now is not wasted time either. I kept all my old notebook pages and looking back, the numbers that mattered were the ones I got wrong first and then chased down. Finding your own mistake in the burn time math teaches you more than copying a worksheet ever woud.

One thing I'd suggest: find out if there's a 4-H or scout group near you that does rocketry, or check if a hobby shop runs build sessions. My shop did a monthly build night and that's where I learned to fillet fins with epoxy properly. Also look at the Team America Rocketry Challenge when you're a bit older, schools form teams and supply the stuff, so age stops being the barrier. Keep the notebook going. When you finally fly your own design and it leaves the rod clean, that first flight beats anything you drew.

I still have my old design notebook from when I was about your age, and honestly the math practice mattered more than I realized at the time. When I finally got to build real kits years later, I allready understood why the center of gravity had to sit ahead of the center of pressure, and that put me ahead of most people at my first club meeting. One thing I'd suggest is plugging your design into OpenRocket, which is free. It'll check your numbers and you can see how changing the nose cone or fin area moves your altitude. My paper designs were always wildly optimistic too, a couple had delta-v figures that would've made it to orbit, but chasing those errors taught me more than the successful flights did.

Funny detail in your post, the fuel lines running through the body tube means you're designing a liquid engine, right? That's way harder math than what most of us started with. Just heads up that hobby motors are all solid, so a scale version would end up looking diffrent inside than your drawings. Doesn't matter for the notebook though. What's the 5km/s figure based on, staging or a single stage?

Gonna push back a bit on the idea that chasing down your own math mistakes is the real learning here. At 11 with no motor data, those burn time numbers are just arithmetic, not design. My kid went through the same phase, page after page of numbers that looked rigorous but were built on guessed weights. What actually taught him something was building a kit and watching the sim prediction miss the actual apogee by a mile. Real hardware gives you feedback a notebook never will. The drawing habit is great, but I'd take one flown Estes over ten pages of consistent numbers.

The reply about the fuel lines being a liquid engine thing is right, and I can confirm the drawing habit pays off either way. I filled a binder with liquid engine sketches around that age too, turbopumps and plumbing everywhere. Years later my first real build was a simple solid kit and it flew fine, but the plumbing drawings taught me to think about where everthing actually fits inside the tube, like how a motor hook and recovery wad have to share space. Ask whoever reviews your numbers to check your mass flow against the thrust and isp togehter, since if those three don't agree the rest of the page drifts. What propellant were you assuming for the 310 seconds?

Update: asked my dad about the club launch idea and he said we can go check one out next month, so that's happening. Also the bit about hobby motors all being solid got me thinking. If a scale version has to use solid motors, do you pick the motor first and design the tube around it, instead of drawing the rocket like I did?