Estimate the number of planes that are in the air in an hour.

1. Considering only domestic flights+ commecial

2. Will not consider military ones

3. Considering all external conditions( weather, delays, etc) fine

Assumptions #1: Though its known that India as ~137 airports in total( but if you do not know then you can guess it)

1. India has around ~800 disctricts

2. All Metro and tier1, tier 2 cities, some tier3 have airports

mathematically: Metro & tier 1 will have 100% airport: 9 cities( bengaluru, kolkata,delhi,mumbai,chennai,hyderabad,ahmedabad,kochi,goa)

Assumption # 2 airport penetration:

Tier 2: 104 cities (70%)= 70

Tier3: ~400 cities(15%)= 60

Total airports: 70+60+9= ~140 airports

Total runways: Delhi has 4 and rest of metro and tier 1 has 2 and 1 airports, that gives us: 17 runways

rest of tier 2 and tier 3 cities airports have only 1 runway= 130 runways

Total runways in india: 130+17= 147 runways

Assumption #3:  if a airplane takes 15 mins to take off, then in an hour 4 airplanes will take off from a single runway.

Total airplabes taking off in an hour = 147*5= 588 airplanes.

So in India in an hour ~600 planes are in air.

How about the approach below?

Task: 

Number of aircraft in the air in a given hour. Assuming all aircraft, globally

Structure: 

- Let's calculate value for commercial aircraft (hypothesis: makes up largest category of planes in air at any given point)

- We can scale-up to all aircraft with a set of broad-stroke assumptions (e.g., % share of total flight time that is commercial / GA / military)

Approach: 

# of commercial aircraft in air in given hour = total # of commercial aircraft * p(air) 

Note: p(air) = probability that a commercial aircraft is in the air at any given time. It is assumed constant throughout the day (though not correct, because population isn't evenly distributed around the world)

So, let's calculate:

- p(air): An average flight is probably ~4 hours long, with a turnaround time of ~2 hours. Assuming planes are 'resting' for ~6 hours overnight (e.g., because no point flying a plane back at night with no passengers), a plane is in the air for ~12 hours per day. p(air) = ~0.5

- total # of commercial aircraft active globally: # of airlines * # of aircraft / airline * % of aircraft in service

• # of airlines - roughly 3 large airlines per country, 200 countries -> ~600 airlines
• # of aircraft / airline - ~40 - very large range here from probably ~500 aircraft on top end to ~1-2 aircraft on bottom end. ~40 aircraft seems reasonable
• % of aircraft active - 80% - need to be high to keep aircraft utilised

Interestingly enough: The real answer (from real data) for commercial aircraft is ~10,000 according to Travel Land Leisure

Give me your feedback on how I would answer this Google estimation question.

Assumptions

1. Will consider planes flying over India only for domestic travel only.
2. Will only consider commercial passenger aircraft. Will ignore military, personal and cargo planes.
3. Will assume that weather conditions are fine all over India & wouldn’t restrict or hamper any airport operations.
4. India has roughly 100 airports form where domestic flight operations occur.

 

The Framework

 

1. We will figure out average number of planes in an hour rather than for a particular hour.
2. Average number of planes in an hour = (Sum of ( Number of planes * duration))/24.
3. For eg if 2 planes fly every hour for 24hrs  a 2hr journey, then the formula would be 2*2*24/24 = 4. The answer is right since we have 2 planes each hour which started their journey this hour & 2 planes which are in air which started their journey in previous hour.

 

Actual Calculations & Assumptions

 

1. Let’s first work on number of planes
   1. Number of planes would be equal to number of runways * number of planes taking off in an hour
   2. For this calculation, we will divide airports into 3 categories :-
      1. Busy - I would say India would have around 8 busy airports. These airports would have 2 runways. These can make a plane fly every 5 minutes and work at 100% capacity.
      2. Intermediate - Around 30 less busy airports. These would have one runway. These can make planes fly every 10 minutes but work at say 50% capacity.
      3. Occasional - around 50 airports which are less busy. These would have one runway. These can make plane fly every half an hour and work at 25% capacity.
   3. Let’s do the calculations for flights in whole day
      1. Busy Airports = 8*2*(60/5)*1*24 = 4608
      2. Intermediate = 30*1*(60/10)*.75*24 = 2160
      3. Occasional = 50*1*(60/30)*.25*24 =  600
   4. So total number of flights taking off in a day are = 7368
2. Now we have to find durations. 
   1. Since it is tough to figure out duration individually, we will take certain assumptions basis the most common sectors of flights
      1. Work related travel - Most of these travels are concentrated around 6-7 big cities. The good things is that for inter-city travel within these cities the flight duration is between 2-4 hrs with 2hrs being the most common (delhi->mumbai, mumbai->bengaluru, delhi->pune etc)
         1. We can assume 75% of all the trips happen due to work relate travel whereas rest 25% is personal.
         2. Within this 75%, we can safely assume that 75% trip happens for 2hrs destinations and for the rest we can take an average
         3. Doing the calculations
            1. Number of work related flights = .75*7368 = 5526
            2. Number of flights with 2hr journey = 5526*.75 = 4145
            3. Number of flights with 3hr journey = 1381
      2. Personal travel
         1. In India, shortest flight duration is 1hr & longest duration is 6hr. But the 6hr flights are not direct. So its very safe to assume that the flights would be in 1-4hr range
         2. Now sake of easiness, we will take some assumptions around these durations
            1. For 1hr flight, the number would be less since people would prefer road transport etc. So we can safely assume that the number of trips with 1hr duration would be less and we can say roughly 10% of the personal trips would be 1hr duration
            2. Now we will equally divide 2&3hr trip since most of the india can be covered within that duration. $hrs flights would again be less. So we assume,
               1. 1hr trips- 10%
               2. 4hr trips - 20%
               3. 2hr trips - 35%
               4. 3hr trips - 35%
            3. Doing the calculations
               1. Number of personal trips = .25*7368 = 1842
               2. Number of 1hr trips = 1842*.1 = 184
               3. Number of 4hr trips = 1842*.2 = 368
               4. Number of 2hr trips = 1842 *.35 = 645
               5. Number of 3hr trips = 1842*.35 = 645
   2. Calculating the total number of hours in a day for all the flights = (4145*2)+(1381*3)+(184*1)+(368*4)+(645*2)+(645*3)=14736
   3. Dividing it by total number of hrs in a day = 14736/24 = 614

 

So we can say that roughly ~600 planes are in air at an average every hour over India.

Note:

If we want to consider international travel, we can use the following logic.

1. Roughly 8-10 airports with international flight operations
2. Most of the flights will cross Indian airspace within 2-3hrs
3. Using the above logic figure out the number of international planes & divide them into 2 & 3hr bucket. 80% would be in 2hr bucket.

 

 

 

Clarifying questions:

1. Planes can be commercial or military. Assuming, in this case, we are referring to commercial passenger flights.

2. We are referring to planes flying over the US area only. 

Equation:

• The number of planes in the air per hour = # of planes taking off per hour from airports across the US

• # of planes taking off per hour from airports across the US = Sum of # of planes taking off split by large, mid, and small airports. 

• Planes taking off an airport = # of runways x (average planes taking off per hour)

• Number of airports in the US: Large, Medium, Small

  • The US has 50 states. It is reasonable to assume there are 2 large/major international airports per state, 15 medium-sized airports, and 10 small airports. 

  • Large airports have 2 runways, medium have 1 runway, small also have 1 runway

  • The average gap between flight take offs in:  

    • a large airport is 5 min during, in medium 10 mins, and 30 mins in smaller 

  • # of planes in 1 hour at:

    • Large Aiport = (2 runway x (60 mins/5 min)  → 24 planes/hour

    • Medium  = (1 runway x(60 mins/10))  → 6 planes /hours

    • Small = (1 runway x (60 mins/30) → 2 planes/hour

  • Number of airports 

    • 50 x 2 large airports → 100 large

    • 50 x 15 medium → 750 medium

    • 50 x 10 small → 500 small

  • The number of planes taking off per hour:

    • Large - (100 x 24) + Medium (750x6) + Small (500x2)

    • ~7000 planes taking off per hour and will be in the air per hour