Here is an easier example.

Think of a truck that sits on a street that is going slightly uphill. There is no way that you and your buddy could lift that truck straight up in the air. But you can relativily easy push it uphill. In the end the truck is going up.

Now, what’s the physics behind that and how does it relate to planes? Well, you don’t have to lift the entire car when pushing. Most of the force from gravity is resisted by the ground. You only have to push against the much smaller horizontal component that tries to push the car downhill.

With planes you basically just replace “ground” by “lift”. So instead of tires pressing against the ground, you have wings pressing against the air. And a jet engine instead of two guys pushing.

Basically a plane’s engines are pushing the plane up a hill made of air.

It’s about lift generation and gravity. Planes stay aloft because of the lift generated. So plane takes off near horizontal, with engines creating thrust in a near horizontal vector. The shape of the wing, combined with the near horizontal thrust vector creates lift, which is perpendicular to the thrust vector, and is what exceeds the pull of gravity, so you climb, while also moving forward. Depending on how you angle the wing, you change that lift force/vector so you can climb, fly level or decend.

If you angle a conventional plane vertically, it will still generate “lift” but that lift will be angled perpendicular to to gravity force. In reality, the plane “stalls” before vertical—this stalling means the wind angle has gone beyond where it can generate enough lift to keep the plane level or climbing. Simply put, most aircraft engines are completely insufficient to escape gravity on their own, they’re using a mechanical advantage via wing generated lift to stay up.

Space rockets use an immense amount of force to escape the atmosphere, they’re basically using a direct vector force to cancel out and exceed gravity, as well as friction. This requires fairly mind boggling amounts of fuel (energy) to do, which is why pounds of cargo capacity are extremely limited.

A VTOL aircraft that has thrust vectoring, can aim thrust down vertically to rise off the ground vertically for a period of time, and then rotate the thrust to the rear to enter into standard lift based flight. I don’t know this exactly, but I suspect the vertical portion of the VTOL sequence is much more energy intensive than the horizontal portion.

Helicopters are neat because they generate vertical lift, but that rotor plane is also capable of behaving like a wing, allowing them to mimic some aspects of fixed wing flight. For instance, if your engine does, you can use autorotation (basically as you fall, it spins the rotors, and you get wing lift so you can “glide” in to land safely).That said, helicopters are less efficient than a fixed wing, which is why if you fly across the country you’re in a large plane, not a helicopter.

I’m sure there are scientific details I’m missing here, but that’s my layman’s understanding of why you can’t point a standard aircraft vertically and fly straight up.

It’s because of the “lift to drag ratio”. Airplanes in level flight at ordinary speeds generate about 15x as much lift as drag meaning if the engine spends 1 unit of work moving the plan forward, the wings give 15 units of work* upwards. So flying level needs about 1/15th the engine power of going straight up. (I’m using “work” very sloppily here, not in a precise physics sense.)

You can see this in sailboats too, which can travel faster than the wind when they’re sailing at an angle to the wind. Efficient boats travel faster when they’re going almost perpendicular to the wind, not straight downwind! This is because the “lift” of the sail pulling the boat forward even more strongly than the push of the wind in the downwind direction.

While I can’t give an intuitive explanation for why this is, there’s a very easy demonstration that it’s true: kites. If a kite had a lift-to-drag ratio of 1, then it would fly at 45° up. It would fly 50 meters downwind of you when it’s 50 meters up. But any decent kite can fly at a much steeper angle than that; sometimes they look like they’re right over your head! That’s because with a lift to drag ratio of e.g. 10, the 1 unit of drag gives 10 units of lift; if it’s 10 meters downwind it will be 100 meters high.

There’s nothing wrong with your reasoning, it just doesn’t account for all of the factors involved. There is a big difference in efficiency between using the forward movement of a wing to provide lift and using direct propulsion pointed downward. There are a few planes that have a greater than 1:1 thrust to weight ratio (the F-15 being the most famous), but it is rare. Fixed wing aircraft and helicopters are all able to fly with less power because what they have is being used more efficiently.

This part is half-right: the work of the engine is going to accelerating the plane forward, or (when thrust and drag are in equilibrium) maintaining the current velocity. But in level flight, the engine is not “keeping the plane in the air” - it is impossible for it to contribute to lift directly because it’s force vector is 90 degrees from the lift vector.

Therefore, some of the engine’s energy is going into keeping the plane in the air, and some is going into accelerating it forwards, or keeping it at the same speed (fighting air resistance).

This is where you make an unsupported leap:

Therefore, if the plane points straight up, the engine should be able to support it hovering in the air. If it didn’t have enough power to fight gravity when pointing straight up, it wouldn’t have enough power to fight gravity when moving horizontally, either.

A car can accelerate horizontally because its engine can rotate its tires to apply horizontal force due to friction and mechanical advantage; does that mean it can drive straight up a wall? Of course not (outside of some specialized bouldering vehicles). The engine lacks the power to lift the car straight up, and the tires lack the grip to hold on to a vertical surface. The drivetrain is designed for efficient road cruising, not high power and grip

It’s the same for aircraft, generally: a given engine usually has enough power to accelerate the aircraft horizontally, and applies this through some kind of prop or jet rotor. But this combination is tuned for efficient cruising, not vertical climbing. The engine won’t provide enough power, and the prop can’t move enough air, to sustain vertical flight indefinitely.

“But Sleet01,” you cry, “helicopters exist!” Just so! They trade cruise efficiency for vertical thrust by greatly increasing the size of the prop, increasing the mechanical advantage so that less engine power is needed to hover or climb vertically. That’s like putting 4" wheels covered in suction cups on your car - now it can go straight up, but you can’t go very far or very fast!

“But Sleet01,” you exclaim, “F-15s exist and can fly vertically almost to space!” Indeed they do, but in order to fly an F-15 vertically you need to burn immense amounts of fuel, almost 400 gallons per minute. That’s like putting two turbo V8s in your Jeep - now you have the power to go vertical, but only for a couple minutes!