Bernie Hoffman of Autonomous Avionics ask and answers the questions about Drones: How high can they go and how much can they carry?
“This question is one of the top three questions I hear on a daily basis. The simple answer is ‘pretty high’, but the reality is much more complex.
To answer correctly, let’s look at this question from a couple of different viewpoints. First, lets look at what is practical, safe, and legal. The FAA wants to limit what a UAV can fly to 400 feet AGL (above ground level). This limit makes sense because it is below most all other air traffic in normal conditions. Obviously aircraft taking off and landing around an airport would be lower, as well as some helicopter operations. From an operations standpoint, operating a small UAV is difficult when it is just a small speck in the sky, and 400′ AGL is plenty for 90% of the pilots and aircraft out there today. My advice: Don’t fly over 400ft AGL.
From a practical standpoint, the physical ceiling of one these aircraft is much higher. The biggest height limitation is the amount of power (in the form of thrust from the propellers) compared to the weight of the aircraft. Normally, the calculation for something like a simple helium balloon would be simple. If the weight of the aircraft is lower than the applied thrust, the aircraft should ascend. For a multirotor, the calculation is a bit more complex. We need not only enough power to lift the aircraft, but we need reserve power in order to keep the aircraft stabilized. As a rule of thumb, the amount of power necessary for a hover should be 50% of the maximum thrust. For our example, lets say the aircraft weighs 2000 grams. In order to hover, we need to develop 2000 grams of thrust just to counteract the force of gravity. To keep everything safe and stable, we need to really create more like 4000 grams of maximum thrust to make this a stable flying aircraft.
What does all of this have to do with the flight ceiling? Well, part of the thrust calculation isn’t just how powerful the motors are, but is, in reality, a calculation that also considers the amount of ‘bite’ the propeller has. At higher altitudes, the air is thinner and the propeller needs to spin faster (or change pitch) to provide the same amount of thrust. So the motors and props have to work harder to maintain the correct level of thrust as the aircraft ascends. We also need to correct for air temperature. Colder air is more dense than warmer air, so our ceiling will also depend on air temperature.
We still have not answered the original question, but let’s look at some anecdotal data. Autonomous Avionics is located in Denver, Colorado. Our ground level is 5,280 feet above sea level. Since we can fly UAVs in Denver, we know the flight ceiling is at least 5,280 above sea level. That means if you are standing at sea level, you can reach at least 5,280 feet.I also have personal experience flying in the mountains. The highest starting point I ever flew started at 13,500 feet and was over 14,000 feet by the time I hit the apex of the flight. So we know from practical experience the flight ceiling is going to be north of 14,000 feet above sea level.
Let’s go back and look at our example.
Aircraft weight (including payload and batteries): 2000g
Total motor thrust: 8000g (at sea level)
This gives a good starting point. I need one other piece of information. Let’s assume at seal level the air pressure is 1000 millibar. At 18,000 feet, the air pressure is only around 500 millibar, so the air density is about half of what we have at sea level. This translates into a maximum thrust of about half of the rating. In our example, the motors would develop only 4000g of thrust, which is right at our threshold for proper flight characteristics of this aircraft.
This simple calculation doesn’t really account for everything but is only a very rough calculation. First, the air pressure curve is not linear. Temperature and humidity are two important factors to also consider and they will influence the air density and lifting capacity as well.
These are some of the starting calculation when determining how high a quadcopter can go. In reality, it really just depends on your aircraft starting weight, what you want to carry and for how long, and how much power (thrust) you have available.”