The fastest production car in the world or the fastest helicopter, I think most of them

would guess the helicopter.

Intuitively we expect anything flying in the air to have a higher top speed than anything

on the ground could achieve, but physics is a cruel mistress and conventional helicopters

are doomed to a max speed of just 400 km/h, with that record being set over 30 years ago

by John Trevor Egginton in a Westland Lynx, while just this year the Koenigsegg Agera

RS demolished that record driving at 445 km/h, and sure you don't have to worry about traffic

in your helicopter or those pesky speed suggestions on the road, but the bragging rights for top

speed will always go to cars for the rest of time.

So how can this be, what quirks of physics are limiting helicopters from flying faster?

First let's look at what limits a cars top speed.

To determine top speed, we first need to identify the forces attempting to slow the vehicle

down.

In space, with no resistance, even a small force can continually accelerate an object

until it reaches close to the speed of light, if it is maintained for long enough, which

would require a silly amount of energy.

On earth though, every time we provide energy to our vehicle, resistance in the form of

air resistance and rolling resistance in the wheels are sapping it away.

Eventually we get to a point where the energy we are providing the vehicle equals the energy

being taken away, and the vehicle cannot travel any faster.

In the case of cars the top speed is predominantly determined by air resistance, for now we will

ignore rolling resistance as it's negligible in comparison.

The equation for drag force is given by this equation, and the equation for power is simply

force times velocity.

Rearranging these variables we get an equation for top speed.

Applying this to the Agera RS specs, we find it's top speed almost perfectly with a decent

degree of accuracy, considering we ignored rolling resistance.

Decreasing our drag coefficient and frontal area also increases top speed, but to increase

power we need to increase airflow to cool the engine, so this is a difficult balancing

act.

We also discovered in a previous video that designing rubber tires capable of withstanding

these rotational speeds is an incredibly difficult task, with the Bloodhound SSC opting for aluminium

wheels to break the land speed record.

These are the limiting factors for a car, so what are the limiting factors for a helicopter.

Helicopters have to deal with all the same problems as cars in counteracting aerodynamic

drag, but first a helicopter needs to overcome the force of gravity, using the same rotor

that will need to provide forward thrust.

So is this just an issue of needing engine power?

Partially yes,

The Westland Lynx was powered by not one but two Rolls-Royce Gem turboshaft engines, each

equaling the power of a single Agera RS twin-turbo V8 engine.

Yet, even with twice the power, it still can't beat it in a straight line race.

How can this be?

Let's go on a journey as the helicopter takes off and transitions to forward flight,

and see why it can't go any faster even with stronger material for blades or more

powerful engines.

As the Lynx powers up the blades begin to rotate faster, providing more lift according

to this equation.

Where A is the swept area of the blades, Cl is the coefficient of lift of the blades and

v is the velocity of the blades.

The coefficient of lift depends on a lot of things, like the geometry of the blades and

angle of attack, but for the sake of simplicity we will assume it is constant.

Once the lift is greater than the weight of the helicopter it begins to rise, and when

it equals the weight the helicopter will enter a hover state.

Now to go forward, the pilot will need to transition some of the lift to thrust by angling

the rotor disk forward.

But here we meet our first problem.

Looking downwards, we can see that left-side of our blade is moving backwards relative

to the the direction of travel, and our right hand side to moving forward relative to the

direction of travel.

Similar to planes, the aerodynamic surface of the blade will generate more or less lift

depending how quickly it is moving through the air.

So our right side generates more lift that our left.

To counteract this the rotor integrates an ingenious little mechanism, where the blade

can change its angle of attack as it rotates.

Here the advancing blade will have a lower its angle of attack, thereby lowering it's

lift, and the retreating blade will increase it's angle of attack, increasing it's

lift.

This helps equalise the lift across the rotor disk, but this solution has it's limit.

As we increase an aerofoils angle of attack the lift increases, but eventually he hit

a point of where flow separation occurs and the aerofoil begins to generate less lift.

This is our first speed limit.

The helicopter will eventually hit a speed where it cannot adjust the angle attack any

further to compensate to dissymmetry of lift.

However there are solutions to this problem.

If we have two blades rotating in opposite directions, we no longer have to compensate

for this dissymmetry in lift, as the two blades will have the opposite dissymmetry of lift

and cancel each other out.

This is what allows the Chinook to cruise along faster than any other military helicopter

at 315 km/h.

Now we have overcome one speed limit, but even now the Agera RS is still speeding ahead

. The next speed limit we reach is the sound

barrier, if we continue to increase forward velocity, the tips of the advancing blade

will eventually break the sound barrier.

And while planes can handle breaking through the sound barrier with the correct design,

they don't need to pass through it several hundreds of times a minute.

This adds to the problems of dissymmetry of lift, but also causes problems with varying

stress that fatigue the material of the blades and ultimately lead to failure.

This speed limit poses a more difficult challenge to overcome in our current configuration.

To travel faster, we need to increase thrust, to increase thrust we need to increase lift.

Let's take a look at the equation from before to see how we can do that.

We can either increase our rotor speed, or we can increase our blade diameter.

Increasing the blade velocity will obviously make us more likely to break the sound barrier,

but so will increasing our blade diameter, as the velocity of the blade increases as

we travel down the blade.

Designers have hit an optimum balance between these two variable already, so that's not

an option for increasing speed.

So how else can we increase helicopter speed?

By converting more of that vertical lift to horizontal thrust, but this poses a new problem,

at some point were are going to hit a point where the helicopter is not generating enough

lift to keep itself aloft.

The solutions to this problem are hitting a point where the we can scarcely call the

aircraft a helicopter.

Enter the Eurocopter X cubed, which holds the unofficial helicopter speed record, unofficial

exactly because it is not strictly a helicopter, as it generates a large portion of it's

forward thrust from vertical propellers.

This decreases the burden of the horizontal rotor to generate forward thrust allowing

it slow its rotational speed, minimising the impact of our previous speed limits, the rotor

can also decrease it's rotational velocity as the helicopter gains speed as more lift

is generated from two small wings on either side of the helicopter.

These design choices allowed the x cubed to reach top speed of 472 km/h, beating the previous

record held by the Sikorsky X2, and demolishing anything ever achieved by a production car.

Pushing this design ideology even further we completely blur the lines of what a helicopter

is, with tiltrotors, like the Osprey.

This aircraft has a top speed of 565 km/h, this combined with it's incredible vertical

take-off capabilities, that are not hindered by limited weight issues like jet engine powered

aircraft like the Harrier, has made it an incredibly versatile tool for the US military.

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