I'll hand it over to Tim for the take-off. Henry will be assisting with all the slides. This is primarily looking at the effect of the massively airborne system on power generation for the EOS system.

So I'll give you the introduction. Henry will take us through a simple Excel calculation so you have an idea of what results you expect. I'll then go through my model method and the inputs I'm using and then compare it to some real-world studies

and then go through some results and conclusions. Well, I'm just being messed up. The point of this is to investigate the massively airborne system and how it affects the power output system. Here I'm going to look at how the power varies

at different time steps through the generation phase and different points throughout the flight. We'll go through a simple Excel calculation and go through more detailed time steps.

Before we get into a detailed model, the first stage is to get a sense of how big this problem is. This is really just a super simple calculation. You've got a kite that's going around. It generates a cycle. The first thing we did was just look at

what the power requirements are to get it up from the bottom of the circle to the top again. So you've got the mass of the kite needs to be taped to the top of the kite. The top of the circle is going back around again. So it's just very quickly the potential energy change and then convert that to a power requirement based on how fast it's going to go around the circle.

I did a couple of examples based on the 20 kilowatt system, which is a lot of the early systems people are using. At 20 kilowatts, if you've got a mass around 25 kilos, it's basically saying the average power you need to input into the kite to get from the bottom of the circle to the top of the circle

is about 3 kilowatts and the peak is about 5 kilowatts. So that's saying basically you're going to get 20 kilowatts plus or minus 5 kilowatts in the circle. Now if you get up to 100 kilowatts, then it's actually about the point where you've got basically zero power as you're going to the top of the circle and you've doubled your power and weight down.

We're kind of interested in how that scales. So if you take it up to a 500 kilowatt system and then a 10 megawatt system, then we can get an idea of what mass is and give that same kind of cycle performance. So 1,000 kilos for a 500 kilowatt system,

you get to about that same point where from a very simple calculation you can see that the power variation is going to be about the same as the power unity in that system. And so in terms of scaling, there's some very rough numbers here. I'm very careful to get more of the masses people are actually thinking that big systems will come to,

but the main issue really is as you get bigger, so there's a square cube rule, maybe you can do a bit better than that with the design and you're not going to end up quite so at that point in power. But ultimately, the key point of this graph is just to show that as systems get bigger, the variation in energy around the cycle is going to get harder to do.

And so that was kind of one of the proven priorities for doing this model and looking at it for the next stage. We'll look at the more in depth matlab model. So it's specifically the system that the range on the ground is going to be operating at a constant tension.

And we'll get a line to be scaled to the single plate system at approximately 10 megawatts raising power, supplying a circuit trajectory for the baseline phase. This model is primarily focusing on the generation phase and restarting what I was thinking because it's going to be quite different depending on what type of system

you're actually going for in the end. And the generation phase is also the main part of the power generation. This input to the model, it's a 10 megawatt rated power system and that's approximately at 12 megawatt per second at kite height.

The tether is 118 millimetres down, so that's a massive tether. And at an average length of 1 kilometre of tether, the kites are 1000 metres squared at a ratio of 10 and the baseline phase is at 35 times that's excluding the tether.

The top section of the tether is going to vary to reduce the drive to 0.1 for our coefficient. So this is the flight trajectory. It's an offset circle about 30 degrees of elevation by upwards in the middle of the wing window and this is to offset

the induction power we get in the middle of the wing window to a more directly down wing at this point. It's got a 400 metre radius which as you can see is quite significant on a 1000 metre tether taking up a very large amount of the wing window.

So the generation phase is modelled by just taking average line length and it does one calculation around the trajectory. This is all done at the 1000 metre line length and the kite parameters of CLT are both fixed and the kite speed is fixed but it's chosen at an optimal kite speed.

I think this is around 80 to 90 meters per second for this case I don't remember exactly. I calculated 16 different points around the flight trajectory for the power curves and then I'm looking more in depth at the trajectory. I'm using 512 points. The tether there's no drag using the catenary

and the wings are basically reduced with the drag model. There's no wind shear in my model but I'm considering induction. There's a paper that Delft put out last year a quasi steady model of

functions like our system. It also provides a couple of models and some experimental data so I decided to compare my model and see how it compares. In terms of modeling methods I've got a dynamic generic trajectory. I'm doing it from different points on Delft papers considering a single point

and just varying the line length at the moment. These track models are very different so here you can see the graphs that have come from the Delft and then in rare my data at the top I took the same inputs to match the data.

As you can see the amplitude of the variations throughout the generation cycle are very similar to X- panels and periods also generally quite accurate. Average power is higher measured experimentally. Probably due to my kind of flying at

fixed CO and fixed CD I think. My model is flying at perfect trajectory so it's a very irregular pattern while in real life. You can see there's a few gaps where the sine wave is obvious of 40 meters squared height

and 20 meters squared height. This is also my model. Here's the panel cover. We've got the baseline system in black and then we've got a 75% version. We've got a 150% and 200%

mass of light as well. Basically as you'd expect the lightest lights generate more power at all wind speeds and less power at all wind speeds and the largest difference in power is at the lighter wind speeds scale the axes so rate of power at one descent

is the rate of power of the baseline system. Now looking just at the generation trajectory so this is like one circular flight path you can see it's quite a large sine wave variation including a large section where it's at negative power

which means the wind is retracting but still at the same constant tension. The main difference is going to be huge gravitational power as we discussed earlier in the Excel model and also the position in the wind window as the flight moves around is less effective wind. I believe there's basically two different sine waves added together

and the mass of the airborne system is affecting the altitude of one of the sine waves and we have a graph of the blue one just the same as the baseline power trajectory around the trajectory and then I'm looking at the gravitational power

which is basically the vertical speed multiplied by the weight of the system and that's in orange and then add them together we can basically see the yellow line is still the oscillation and this oscillation matches pretty closely the effective wind speed

or effective wind power effective wind speed cubed due to the different position around the wind window there's a slight variation I believe it's just due to the rolling angle varying as we can see this is taking the minimum, maximum

and mean of the previous sine wave and then looking at different heights into the wind speeds this is a particularly nice looking graph in that you get into negative line speeds for all cases except the highest wind speeds for the lightest case

so the winch is going to be reversing and changing direction during the generation which is not good for the winch it's a completed design and we're seeing topics for the winch and it's going to be at the same point

it's kind of hidden behind the table so basically the scale of the winch based on 50% 50% capacity factors looking at how the mass of the system affects the roll capacity factor

and as you expect at the higher wind sides the mass has a smaller difference you can gain 3% by halving the mass at the higher capacity factor but at the lower capacity factor you're going to gain 6%

also looking at the terms of flight paths here we're reducing 96% of the launch power so a bit less power but the main positive thing is that the power stays positive throughout the alternating treatments which means that the winch

comes to pretty much a standstill at the upwards point in the flight trajectory you always have a downside you figure out the empty roll in one direction and the roll in the other direction conclusions I was quite happy with how the model

matches the experimental data for small scales both in the amplitude and the periods the overestimate the power quite a little bit I think this is a good first use tool to get an idea of what to expect

increasing mass obviously a very big impact on LCD maybe less yield at more cost operating cost of replacing the maintenance in the winch and just requiring a more complex winch design initially and we've seen that flying alternative flight paths

there is optimization to be had further work I'd like to look at more flight path optimization the circle different variations and also having looked at the bearing elements here I've kept constant

flight tensions after flight trajectory other options are bearing the mind tensions and bearing the mind speeds then I'd like to reduce the overall power spikes you can also vary lift and drag against kites in the history of the study

further, like the bench effect is similar to the LCD model where you can look at more optimized kite design a smaller kite that's generating the same power as the larger kites and eventually see how this will impact the power curves