**1. Introduction**

So I’m a subscriber to *the Hacksmith* youtube channel, which is a guy who tries to bring superhero devices into the real world. It’s been a while he’s working on the development of the “Flying like Iron Man” project, which is a quite difficult and money-hungry project. Although I’m not quite a fan of the methods that are shown in the channel for the engineering of such a complex device, I also bear in mind that the audience would probably find the engineering details quite boring and unrewarding, so the progress updates are more on the testing side than on the design side.

Anyways, he started a crowdfunding campaign on GoFundMe, which means that this might get serious. Although I can’t contribute due to the fact I’m back in Brazil (and here our money is worth quite a lot less than in those developed countries), I thought it might be interesting to give a review on this project. So sorry, *the Hacksmith*, but this is all I have to offer… =/

I remembered that I made a while ago a spreadsheet to determine the rotor diameter for a personal one-seater electric helicopter for a senior design project class. As the spreadsheet was ready to go, it wasn’t that much trouble to plug in the numbers for his design. You can download it here, if you want to play with it. It’s not a great spreadsheet, though, and its far from a polished user-friendly status that I normally take my spreadsheets to.

**2. The helicopter equation**

The jetpack, the helicopter, the drone and the rocket are vehicles that have something in common: They need to stay afloat by pushing a fluid downwards. The airplane stays afloat in the same fashion (by pushing air down), but it does so with its wings by moving forwards.

But what’s the difference? Well, it requires quite a lot of energy to push enough of a light fluid (such as air) to generate any decent lift. You can see, for example, that a water jetpack is much smaller and feasible than an air-hovering one. It has to do with the fact that in order to get thrust you need to pump mass (as momentum is ), which results in a much larger device if the fluid being pumped has little density (as is the case for air).

The problem becomes even more important when we account for energy. As anything that stores energy (fuel or batteries) has mass and needs to be carried with the hovering device, there is only so much of it that you can bring with you. The amount of mass will depend on how much time you want to stay hovering in the air. For a helicopter or any hobby drone, it’s desired to stay hovering in the air for at least 20-30 minutes, so one can get from point A to B. The more you want to stay in the air, the more energy you’ll need to bring with you. But then you become heavier, and will need to bring even more energy to stay afloat. How can one assess whether this will result on an endless loop?

Well, there comes the helicopter equations to help us, designers. I selected the set of equations shown below, which are useful for solving a battery-powered hovering device. Since it assumes no relationship between the mass of the engine/thruster and its size/power, it’s really only useful within a limited range of powers and fan diameters. But it will be enough to show the point I want to make:

*[Lift equation]*

* [Power needed to displace the fluid]*

* [Total mass of the hovering device]*

* [Stored energy in the battery]*

* [Total flight time to discharge battery]*

* [Relationship between mass flow and volumetric flow]*

Solving the equations above for leads to this very interesting relationship:

Although that equation looks scary, some lessons can be extracted from it:

- The diameter of the fan is directly proportional to the flight time
- It’s inversely proportional to the battery energy density , which means better batteries will have a direct impact on the fan size
- The diameter of the fan has this complex relationship with the battery mass . But it basically means the following: If you were to reduce the battery mass down to zero, the diameter of the fan would need to be infinity (which is quite unfeasible). If the battery mass is very large, then the relationship is between linear and quadratic ( ). If, on the other hand, it’s in the middle, then there is a minimum diameter.

The minimum value of will be possible only when:

Which is surprisingly simple! This leads to a minimum diameter of:

Unfortunately, normally that’s a lot of batteries. Therefore, the best choice normally is not the minimum diameter. Also, for the case in analysis, it would lead to a supersonic exit speed, which throws all the equations shown here through the window…

**3. So, is it possible to fly like Iron Man?**

Yes, it indeed is possible to do so. It’s not some crazy stuff, and *the Hacksmith* data seems to be accurate and adequate. The spreadsheet I linked in the first section is based on his data. So what does the graph of diameter versus battery mass look like for *the Hacksmith’s* design?

This curve was generated for a device that uses 6 EDFs. It seems that he will be able to hover just a little bit less than 2 minutes, which also corresponds to the claims in his GoFundMe campaign. So it seems legit, although it wouldn’t be very fit for a transportation device. If he wanted more hover time, it’s just a matter of increasing fan size or transporting more batteries. Or both!

For this calculation I considered a fan energy conversion efficiency of 50%, but the fans linked in his campaign page seem to claim an efficiency of 70% (which seems kinda too much for these devices). So there might be some difference between calculations and reality, but that’s exactly what engineering boils down to anyways!

So I hope this helped you to understand the underlying principles with a benchmark case. I hope you guys at* the Hacksmith* channel actually manage to build it! I’ll definitely stay tuned!