Looking for games in which you can construct your own aircraft

Space Engineers

SimpleRockets?

Don't think this is what you're looking for since it's probably much faster paced than what you want but, Captain Forever Remix

Kerbal Space Program. I know it's mostly about exploring and all, but you can also build airplanes to explore the game's earth.
Edit: sorry only read the title :C

I'm not 100% sure but I think Cargo! The Quest for Gravity lets you build flying machines later on?

Reassembly mentions Spaceship building
Maybe Autocraft but it's stuck in EA.
Gray area , not sure about this Gimbal,
and This lets you swap airplane parts probably not what you'd want though: LUFTRAUSERS

You can also build an aircraft in Besiege and Homebrew - Vehicle Sandbox.

TerraTech
http://store.steampowered.com/app/285920/

From the Depths
http://store.steampowered.com/app/268650/

And possibly Empyrion
http://store.steampowered.com/app/383120/

Cargo! - The quest for gravity ;P

Any other suggestions guys?

Banjo-Kazooie Nuts&Bolts

Nah, just kidding, that game is horrible. Tried the final stage of Spore? Or Fractured Space?

From the Depths
http://store.steampowered.com/app/268650/

There was a plane one but can't remember the name that isn't simpleplanes.

[Edit] AX:EL - Air XenoDawn http://store.steampowered.com/app/319830/

Seems nice (never tried it myself)
Good reviews
Multiplayer
Cheap