The air particles hit the aircraft with the same force, but in a given amount of time, more of them hit it.
The above statement is not strictly correct.
It would be more accurate to say that at the higher altitude the individual particles hit the aircraft with greater force (because the TAS at any given IAS is greater), but because the air is less dense, less particles hit the aircraft.
The Airspeed Indicator (ASI) is simply a pressure instrument which measures the dynamic pressure, 1/2 Rho V squared, Where Rho is air density and V is the TAS. Every time the ASI senses a given value of dynamic pressure it will give the same indication (IAS).
So flying at different altitudes at constant IAS means that we are flying with the same dynamic pressure. But because the air becomes less dense as our altitude increases, we require a greater value of TAS to achieve the same dynamic pressure.
If for example the value of Rho at the higher altitude is 1/4 of the value at the lower altitude, then the value of V squared at the higher altitude must be four times that at the lower altitude. To increase V squared by a factor of four we must increase V by a factor of 2. So although our IAS remained constant, our TAS at the higher altitude must be twice that at the lower altitude.
Do you agree on the fact that IAS (then parasite drag) is determined by the force with wich the air particles strike the aircraft, and not the amount of air particles ? Instinctively, I would think that if more particles hit the Pitot tube, the pressure felt would increase (and IAS increase as a consequence).
The force exerted by the airflow is determined by the force exerted by each individual particles and the number of particles hitting the aircraft in a given time. As I have explained above, if the IAS is constant then the dynamic pressure must also be constant.
It takes more fuel to indicate 300 kts at 10000 feet than at 5000.
We need to be careful here. We are talking about 300 Kts IAS, so the dynamic pressure and drag will be the same at both altitudes, so the thrust required will also be the same at both altitudes. But the amount of fuel flow required to produce this thrust will also be influenced by the type of engine, the varying specific fuel consumption and the varying propulsive efficiency.
In piston engines fuel flow is proportional to power, but in jet engines fuel flow is proportional to thrust. So in a jet aircraft fuel flow at the two altitudes would be about constant (as observed by Capt Bloggs). But in a piston aircraft more fuel flow would be needed to provided the increased power required to maintain the higher TAS.
Capn Bloggs
Blogg's jet science: Drag requires Energy to be used = fuel burnt. Drag, roughly speaking, ismostly created by IAS.
That is correct, but we need to remember that not all of the fuel burned is converted into thrust and power.
At 250KIAS at Sea Level (TAS around 250), I use about 2100kg/per hour. N1 is way down, around 60%
At 250KIAS at FL300, I will still use around 2100kg/hr, but TAS is around 400. N1 is way up, around 85%.
As I have explained previously, constant IAS means constant dynamic pressure and this means constant drag. So yes your fuel flow may have remained approximately constant. But this does not mean constant power output. The constant drag required constant thrust and in jet engines fuel flow is proportional to thrust. But it is not proportional to power. As you climbed at constant 250 kts IAS your TAS increased while drag remained constant. Propulsive power required is drag times TAS, so as you climbed the power output must have increased. So although your fuel flow was constant so power output increased.
If 3.375 times the power is required at FL300, there would be no point in going high at all. You only get a 80% increase in speed. Far cheaper (but longer) to fly low.
Let’s test your argument over a distance of 2000 miles, using the figures you have given.
MSL 5000 nm / 250 kts = 20 hours. 2 hours x 2100 kg/hr = 42000 kgs
FL300 5000 nm / 400 kts = 12.5 hours. 12.5 hours x 2100 kg/hr = 26250 kgs.
So flying at MSL used an extra 15750 kgs of fuel and took and extra 7.5 hours.
My understanding is that the V in the drag formula is velocity with respect to the air the aircraft is in, ie IAS, not TAS.
I think that you need to read that again. The velocity with respect to the air is the TAS. The IAS is just an indication.
The power required at Seal levl and FL300 for the same IAS is roughly the same.
You are just plain wrong her. The points that you are missing are:
1. Fuel flow in jet engines is proportional to thrust and is not proportional to power.
2. As altitude increases at constant IAS, the drag is constant, so the thrust required
is constant. This should mean that fuel flow is also constant, but see other
factors listed below.
3. As altitude increases the specific fuel consumption decreases, thereby reducing
the fuel flow required to maintain constant thrust.
4. As altitude increases the propulsive efficiency increases thereby reducing the
amount of energy that is being wasted in the exhaust gasses.
5. As altitude increases at constant IAS the TAS increases thereby reducing the time
taken to cover a given distance.
6. As altitude increases items 4 and 5 above enable the engines to produce the higher
power that is required, without increasing the fuel flow.