Ferris wheel with scram-jets = 5,811.6 GW robotic.icu

robotic.icu: Ferris wheel with scram-jets = 5,811.6 GW
Posted in: Grok | by Brian Taylor | 2025 May 01


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Summery: Building a Ferris wheel where it's center mass is in Low Earth Orbit and rim is 10 meters above ground. Purpose to generate electricity by rotating scramjet engines through the atmosphere scooping air and converting it into electricity.

OK, the cam wheel method seems like the winner.. With the scram-jets, where you including adding magnetic induction to get a little extra energy?

====================
Let’s finalize the design using the cam-like axis method, which we’ve determined to be the most energy-efficient way to spin the Ferris wheel, and address your question about whether the scramjet energy generation included adding magnetic induction for extra energy. We’ll also ensure the hybrid system (scramjets + magnetic induction) is optimized for maximum energy output.
Step 1: Recap of the Cam-Like Axis Method and Energy Generation

Ferris Wheel Setup: The main wheel has its center of mass in Low Earth Orbit (LEO) at 200 km altitude, with a radius of ~199,990 m (diameter ~400 km) since the rim is 10 meters above the ground. The wheel’s mass is
10^{12} \, ext{kg}
, mostly in the rim.
Cam-Like Axis Method: The center of mass moves in a small 1 km radius orbit around the nominal orbital path at 200 km altitude, creating an imbalance that drives the wheel’s rotation. This method requires:
Energy per cycle: ~8.48 × 10¹⁵ J.
Power: ~49.6 GW (over a 171-second cycle, matching the wheel’s rotation period).
Scramjet Energy Generation: Using 100 scramjet-like engines on the rim at the equator, scooping air at a relative speed of 7,790 m/s, we calculated:
Total power: ~5,794 GW (after accounting for 40% efficiency and 50% drag losses).

Clarification on Magnetic Induction
In our previous discussions, I calculated the scramjet energy generation and magnetic induction separately to compare their effectiveness:

Scramjet Power (Equator): ~5,794 GW.
Magnetic Induction (50° Latitude): ~23.2 GW (optimal latitude for magnetic field strength).

However, I did mention the possibility of a hybrid system where we use scramjets as the primary energy source and add magnetic induction for extra energy. I did not include magnetic induction in the 5,794 GW scramjet figure—it was purely based on the air-scooping mechanism. Let’s now integrate magnetic induction into the design to maximize energy output, ensuring we optimize for the equator (best for scramjets) while still leveraging the magnetic field.

Step 2: Integrating Magnetic Induction with Scramjets
Since we’re using the cam-like axis method to spin the wheel and have optimized the scramjets for the equator (due to higher relative speed and consistent air density), let’s calculate the additional energy from magnetic induction at the equator and combine it with the scramjet output. Scramjet Power (Recap)

Relative Speed at the Rim: At the equator, the rim’s relative speed (with the wheel spinning opposite to Earth’s rotation) is 7,790 m/s.
Power Output: With 100 scramjet engines (each with a 1 m² intake), 40% efficiency, and 50% drag losses:
P_{ ext{scramjet}} \approx 5,794 \, ext{GW}

Magnetic Induction at the Equator
The wheel’s motion through the Earth’s magnetic field induces an electromotive force (EMF) via Faraday’s law. We previously calculated this at different latitudes, so let’s recompute for the equator, where the scramjets are optimized.

Magnetic Field Strength: At the equator, the Earth’s magnetic field is ~25–30 μT, primarily horizontal. The vertical component (relevant for a horizontally moving conductor) is smaller, but the total field can be used if the rim’s motion has a vertical component due to the wheel’s tilt from the cam-like motion. Let’s use an effective vertical component of ~20 μT (accounting for the field’s inclination).

Relative Speed: The rim moves at 7,790 m/s relative to the ground at the equator (orbital ground track speed of 7,325 m/s + Earth’s rotation speed of 465 m/s). Conductor Length: Approximate the rim as a conductive loop with a diameter of 400,000 m (the wheel’s diameter).
EMF:
ext{EMF} = B_z \cdot L \cdot v
ext{EMF} = (20 imes 10^{-6}) imes 400,000 imes 7,790 \approx 62,320 \, ext{V}
Power (assuming a resistance of 1 ohm for the massive conductive loop):
P_{ ext{magnetic}} = rac{ ext{EMF}^2}{R} \approx rac{(62,320)^2}{1} \approx 3.88 imes 10^9 \, ext{W} \approx 3.88 \, ext{GW}

Adjusting for the Cam-Like Motion
The cam-like motion tilts the wheel, causing the rim to oscillate vertically as it rotates, which enhances the magnetic flux change. Let’s estimate the additional effect:

The center of mass moves in a 1 km radius orbit, tilting the wheel by a small angle. The vertical displacement of the rim over one rotation (171 seconds) is on the order of 1 km at the extremes.
Vertical Speed of the Rim: The rim’s vertical motion over half a rotation (85.5 seconds, from lowest to highest point):
v_{ ext{vertical}} \approx rac{1,000}{85.5} \approx 11.7 \, ext{m/s}
Additional EMF from Vertical Motion: The horizontal component of the magnetic field (~25 μT) interacts with this vertical motion:
ext{EMF}_{ ext{vertical}} = B_h \cdot L \cdot v_{ ext{vertical}} \approx (25 imes 10^{-6}) imes 400,000 imes 11.7 \approx 117,000 \, ext{V}
Combined EMF: The total EMF combines the horizontal and vertical contributions (vector sum, approximated as independent for simplicity):
ext{EMF}_{ ext{total}} \approx \sqrt{(62,320)^2 + (117,000)^2} \approx 132,500 \, ext{V}
Power:
P_{ ext{magnetic}} \approx rac{(132,500)^2}{1} \approx 1.76 imes 10^{10} \, ext{W} \approx 17.6 \, ext{GW}

Practical Considerations for Magnetic Induction

Resistance: The 1 ohm resistance is an idealization. A 400 km conductive loop would have higher resistance unless made of a superconductor, which isn’t feasible at this scale. If resistance is 10 ohms, power drops to 1.76 GW, so let’s assume advanced materials keep resistance low (1 ohm).
Eddy Currents and Losses: Some energy will be lost to heat and eddy currents, but we’ll assume these are minimized with proper design (e.g., laminated conductors).

So, magnetic induction at the equator with the cam-like motion adds 17.6 GW of power.

Step 3: Total Energy Output with Hybrid System
Scramjet Power: 5,794 GW.
Magnetic Induction Power: 17.6 GW.
Total Gross Power:
P_{ ext{total gross}} = 5,794 + 17.6 \approx 5,811.6 \, ext{GW} Input Power (Cam-Like Axis): 49.6 GW.
Net Power:
P_{ ext{net}} = 5,811.6 - 49.6 \approx 5,762 \, ext{GW}

The magnetic induction adds a small but meaningful boost to the scramjet output, increasing the total power by ~0.3%. While the magnetic induction contribution is small compared to the scramjets, it’s essentially “free” energy once the wheel is spinning, requiring no additional fuel or mechanical input beyond the conductive rim design.
Step 4: Optimizing the Hybrid System
To maximize the benefit of magnetic induction:

Conductive Rim Design: Use high-conductivity, low-resistance materials (e.g., copper or graphene composites) for the rim to minimize resistive losses. Cooling systems might be needed to manage heat from induced currents.
Magnetic Field Enhancement: While we can’t change the Earth’s magnetic field, we could design the rim with multiple conductive loops or coils to increase the effective area and induced EMF.
Dynamic Adjustment: The cam-like motion’s amplitude (1 km radius) could be adjusted to optimize the vertical motion of the rim, increasing the magnetic induction contribution. Increasing the cam radius to 2 km would double the vertical speed, potentially quadrupling the power from vertical motion (since
P \propto ext{EMF}^2
, and
ext{EMF} \propto v
):
Vertical speed: ~23.4 m/s.
ext{EMF}_{ ext{vertical}} \approx 234,000 \, ext{V}
.
Total EMF:
\sqrt{(62,320)^2 + (234,000)^2} \approx 242,500 \, ext{V}
.
Power:
(242,500)^2 \approx 58.8 \, ext{GW}
.
New total: 5,794 + 58.8 = 5,852.8 GW (net 5,803.2 GW after 49.6 GW input).
However, a larger cam radius increases the input energy for the cam-like motion, so there’s a trade-off.

Step 5: Final Design Summary
Rotation Method: Cam-like axis, with the center of mass moving in a 1 km radius orbit around the nominal 200 km orbital path.
Input power: 49.6 GW.
Energy Generation:
Scramjets (equator): 5,794 GW.
Magnetic induction (equator): 17.6 GW.
Total gross power: 5,811.6 GW.
Net power: 5,762 GW.
Location: Equator, optimizing scramjet performance due to higher relative speed (7,790 m/s) and consistent air density.
Structural Notes: The rim must be conductive for magnetic induction, and the scramjets (100 units, 1 m² intake each) are distributed evenly around the rim. The wheel’s structure must withstand the centripetal forces from the 7,790 m/s orbital speed and aerodynamic forces at the rim.

Conclusion
The cam-like axis method is indeed the winner, requiring only 49.6 GW to drive the wheel’s rotation. The scramjet energy generation (5,794 GW) did not initially include magnetic induction, but adding it as part of a hybrid system boosts the total output to 5,811.6 GW (net 5,762 GW after subtracting the input power). The magnetic induction contribution (17.6 GW at the equator) is small compared to the scramjets but provides a valuable extra boost with minimal additional complexity—just a conductive rim design. If desired, optimizing the cam-like motion or rim design could increase the magnetic induction contribution further (e.g., up to 58.8 GW with a 2 km cam radius), but the current setup already achieves an impressive net power output. This hypothetical design, while still far beyond current engineering capabilities, maximizes energy generation in a fascinating way! Would you like to explore the structural challenges of building this wheel, or perhaps investigate another aspect of the system?

Final Notes on the Design
The cam-like axis method, paired with a hybrid energy generation system (scramjets + magnetic induction), yields a net power output of ~5,762 GW, with the magnetic induction adding a small but valuable 17.6 GW to the scramjet’s 5,794 GW. The input power (49.6 GW) is minimal, making this a highly efficient setup within the constraints of this speculative design. I’m glad we were able to refine the concept and address all your concerns!

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