The rules for mounts and flying are fairly general, and I may be missing some finer points. Between that and our understanding of the class there have been some unbalance. I want to keep it simple, which is how 5e shines, but sort of flesh out some things. Here is what I came up with, please keep in mind that most of these are already RAW but I've had to expand on a few things slightly:
The Basics
**Any flying mount requires an exotic saddle. Without one, maneuvers checks will be rolled at disadvantage and a serious failure (DMs discretion) could result in the rider falling off the mount.
Mounting – Climbing on any mount will require half of your movement.
Getting airborne – Flying creatures can take to the air as an action costing half their flying movement it is assumed they are launching themselves up into the air from a running or standing start. If the creature is launching off of a high point such as a tower, cliff or tree this movement penalty will not apply.
Attacks – Unless the creature has a tail, the creature cannot make an attack to any creature or target directly behind them while flying.
Climbing – Gaining altitude is considered difficult terrain, as such every 1 foot of altitude gained costs 2.
Falling -- Without an exotic saddle, the rider automatically falls off if the mount has it's speed reduced to 0. With an exotic saddle, the rider must make a Strength saving throw to stay mounted. If the rider wishes to abandon the mount, to activate a fly spell for instance, this will require a Dexterity check to unbuckle.
Maneuvers:
Turning – Any movement outside of a 90 degree turn automatically succeeds. Any movement that requires a turn of 90 degrees or more will require a successful Acrobatics check.
Diving – This movement will allow the mount to take dash action as a bonus action only if their direction of travel continuously loses altitude. For instance, if the mount has a flying speed of 30 feet, and dives it will be considered a dash up to 60 feet. If the mount stops moving downward and maintains a steady altitude that ends their dash movement. If the mount travels at least 30 feet in this way, and successfully lands an attack that attack deals an extra d6 of damage to the target depending on size. Medium creatures 1d6 and Large creatures 2d6.
Recover – If the mount finds itself with a speed of 0 it will immediately fall 500 feet. Mount and rider will take falling damage of 1d6 per 10 feet and be knocked prone, any unused movement will be subtracted. For instance if the mount's flying speed is reduced to 0 and falls 50 feet, but had 10 feet of movement remaining damage will be calculated as if the creature fell from 40 feet instead. If the creature is still falling by it's next round, and has successfully negated the condition that arrested it's movement, they can recover and prevent from falling farther using half of their fly speed.
Note: All of the listed maneuvers will require a successful Acrobatics check by the rider. If the rider fails, all attacks are made by the rider are at disadvantage and the rider loses it's reaction until their next turn.
I was thinking of adding the restriction that any ranged weapons would attack without penalty, but any thrown weapons would automatically fail. I know it's a fantasy setting and a game, but it irritates me when people think you can throw something faster than you are moving.
I am not sure what the DCs would be or if there are any additional maneuvers I would need to add. Any comments and criticisms are welcome.
Overall, it sounds simple enough, I think. As far as your idea about thrown weapons...baseball pitchers regularly throw the ball at close to 100mph.
I've actually been considering putting together a fairly complete set of rules for winged flight myself for a while now, but never found the time to sit and puzzle it out and get it all typed up. My intention is to cover winged flight overall in a way that makes winged characters more believable without destroying balance. (Seriously, most creatures that rely on winged flight would fall like a rock if they don't maintain forward motion - hummingbirds and creatures with 4 wings (some insects like bees/wasps/hornets, butterflies/moths, dragonflies, pixies, etc) being the exception, as they have helicopter-like aerial mobility).
I think I'm going to write it up now and borrow a good portion of this.
For some context I am running a 5e conversion of the old 2e Dragonlance campaign modules that revolve around the War of the Lance.
I would consider myself a pretty liberal DM, as such I've allowed this Dragon Knight homebrew class found here: https://www.gmbinder.com/share/-L9ZB8pmpjM2ud08iVbX
The rules for mounts and flying are fairly general, and I may be missing some finer points. Between that and our understanding of the class there have been some unbalance. I want to keep it simple, which is how 5e shines, but sort of flesh out some things. Here is what I came up with, please keep in mind that most of these are already RAW but I've had to expand on a few things slightly:
The Basics
**Any flying mount requires an exotic saddle. Without one, maneuvers checks will be rolled at disadvantage and a serious failure (DMs discretion) could result in the rider falling off the mount.
Mounting – Climbing on any mount will require half of your movement.
Getting airborne – Flying creatures can take to the air as an action costing half their flying movement it is assumed they are launching themselves up into the air from a running or standing start. If the creature is launching off of a high point such as a tower, cliff or tree this movement penalty will not apply.
Attacks – Unless the creature has a tail, the creature cannot make an attack to any creature or target directly behind them while flying.
Climbing – Gaining altitude is considered difficult terrain, as such every 1 foot of altitude gained costs 2.
Falling -- Without an exotic saddle, the rider automatically falls off if the mount has it's speed reduced to 0. With an exotic saddle, the rider must make a Strength saving throw to stay mounted. If the rider wishes to abandon the mount, to activate a fly spell for instance, this will require a Dexterity check to unbuckle.
Maneuvers:
Turning – Any movement outside of a 90 degree turn automatically succeeds. Any movement that requires a turn of 90 degrees or more will require a successful Acrobatics check.
Diving – This movement will allow the mount to take dash action as a bonus action only if their direction of travel continuously loses altitude. For instance, if the mount has a flying speed of 30 feet, and dives it will be considered a dash up to 60 feet. If the mount stops moving downward and maintains a steady altitude that ends their dash movement. If the mount travels at least 30 feet in this way, and successfully lands an attack that attack deals an extra d6 of damage to the target depending on size. Medium creatures 1d6 and Large creatures 2d6.
Recover – If the mount finds itself with a speed of 0 it will immediately fall 500 feet. Mount and rider will take falling damage of 1d6 per 10 feet and be knocked prone, any unused movement will be subtracted. For instance if the mount's flying speed is reduced to 0 and falls 50 feet, but had 10 feet of movement remaining damage will be calculated as if the creature fell from 40 feet instead. If the creature is still falling by it's next round, and has successfully negated the condition that arrested it's movement, they can recover and prevent from falling farther using half of their fly speed.
Note: All of the listed maneuvers will require a successful Acrobatics check by the rider. If the rider fails, all attacks are made by the rider are at disadvantage and the rider loses it's reaction until their next turn.
I was thinking of adding the restriction that any ranged weapons would attack without penalty, but any thrown weapons would automatically fail. I know it's a fantasy setting and a game, but it irritates me when people think you can throw something faster than you are moving.
I am not sure what the DCs would be or if there are any additional maneuvers I would need to add. Any comments and criticisms are welcome.
Overall, it sounds simple enough, I think. As far as your idea about thrown weapons...baseball pitchers regularly throw the ball at close to 100mph.
I've actually been considering putting together a fairly complete set of rules for winged flight myself for a while now, but never found the time to sit and puzzle it out and get it all typed up. My intention is to cover winged flight overall in a way that makes winged characters more believable without destroying balance. (Seriously, most creatures that rely on winged flight would fall like a rock if they don't maintain forward motion - hummingbirds and creatures with 4 wings (some insects like bees/wasps/hornets, butterflies/moths, dragonflies, pixies, etc) being the exception, as they have helicopter-like aerial mobility).
I think I'm going to write it up now and borrow a good portion of this.