I wonder if a jet plane can have helicopter rotor for vertical take off and then, when moving forward just stops that rotor and uses lift from wings like normal plane.
Since rotor blade seems thinner and smaller than wings, I guess when turned off, its drag should be much lower than wing.
So why doesn't that type of hybrid plane exist?
Or the drag of the rotor at the jet speed would be so high? If the drag is high, why is it high, since the rotor blade is also airfoil like wing?
There were actually some experiments with stopped rotor. Furthest with the actual implementation was probably the Boeing X50 Dragonfly:
By Source, Fair use of copyrighted material in the context of Boeing X-50 Dragonfly
The main reasons I can think of why nothing like this reached production yet are:
When the rotor spins, the blade on one side moves aft and needs to have its leading edge face aft, but when the rotor is stopped, both sides need the leading edge facing forward. So either the airfoil must be symmetric, but that has really poor efficiency, or some blades have to turn somehow, which is complicated.
To be light, rotor blades are normally very flexible and rely on the centrifugal force to keep them straight under load. But when they stop, they won't have such force, so they must be much stiffer, which makes them bit too heavy to spin.
Having separate wings and rotor would add a lot of weight, especially since the rotor would still have to be made strong enough to resist the aerodynamic loads when stopped.
So why doesn't that type of hybrid plane exist?
This type of plane does not exist largely because there is a simpler way to go about this that has already been done with some success. Planes like the Harrier are capable of VTOL by simply re-directing the exhaust of the jet.
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In this case you reduce the amount of moving parts by not needing both a regular jet system and a helicopter mechanism (which requires a lot of up keep) instead its simply easier to have a directed nozzle
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This idea has been carried over into the prop world with Boeings V-22 Osprey which has tilt control rotors that allow for VTOL but are also used for forward flight. In this case
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To directly answer the drag question, yes the drag would be high (some one else may be able to provide a specific number or the math) but like anything else the design could be built it just would not be very efficient. Since you can generally control the pitch of a helicopter rotor you could potentially (on an even numbered rotor system) orient at least 2 of them to act like small wings and generate very limited lift to assist you even in their static situation.
Like most things in aviation planes are built for a given mission profile. VTOL fits certain cases like anding on an aircraft carrier or in other hard to reach places but things like commercial planes already have a large runway based infrastructure to support them. Any hard to reach place that you need to land at most likely also means your loads are small and a helicopter will suffice, you would need a large hard to reach place that had constantly large loads going in and out to justify a sizable commercial plane that had VTOL capability. While there are some applications for this in the military space (carrier landings come to mind) there are other systems that have been found to be efficient to use. Interestingly enough the directed exhaust from the new F-35's has caused issues on the deck of aircraft carriers.
Anything that uses a rotor to take-off vertically is most inefficent when lifting, hovering or moving slowly. This is most obvious when a helicopter is at max weight or in "hot and heavy" conditions when it might not be possible to take-off vertically.
In order to lift vertically, thrust must be greater than weight. This is not true for a "conventional" aircraft.
If you use a rotor only for lifting off, then that rotor becomes nothing but extra weight (and complexity) that you don't need. Maybe you could use the stopped rotor to generate some lift in a similar fashion to a conventional wing but as others have pointed out, to make a rotor blade which is rigid enough to act as a static wing and can still handle the forces generated when rotating is a serious engineering challenge that will add more weight and complexity (because the rotor hub must have hinges that can absorb the forces when rotating but keep the blade rigid when stationary).
You also need some complex, and therefore heavy, mechanism for tranisitioning the thrust from the rotor whilst lifting to whatever propulsion you use for forward flight.
More weight, more complexity, more maintenance, more cost, more to go wrong. What's not to like? ;)
The other answers also point out better solutions such as vectored thrust and using the same rotors to lift and to provide thrust in forward flight.
Add this all together and you have a solution for a problem which doesn't exist.
