Your question touches on **aerodynamics, gravity, and the "8 inches per mile squared" curvature claim**—a common point of debate. Let’s break it down rigorously.

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### **1. The "8" per Mile² Curvature Myth**  
- **Claim**: Earth’s curvature drops 8 inches per mile squared (a simplified approximation).  
  - Formula: \( d = \frac{h^2}{2R} \) (where \( R = \) Earth’s radius).  
  - For 100 miles: \( d \approx 6,667 ft \) of drop (not linear).  
- **Reality**: This is a **geometric calculation**, not a physical force pilots must "adjust for."  

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### **2. How Planes Stay Level**  
#### **A. Gravity Acts on the Entire Plane**  
- Gravity **does** pull the entire plane equally (nose, wings, tail).  
- But planes maintain altitude via **lift** (aerodynamic force opposing gravity).  

#### **B. No "Nose-Dip" Needed**  
- **Reason 1**: The plane follows Earth’s curvature **automatically** because:  
  - Gravity is **always** pulling toward Earth’s center (not "down" in a straight line).  
  - The wings’ lift adjusts **continuously** to match the curved path.  

- **Reason 2**: The curvature is **too gradual** to require manual adjustment.  
  - At 500 mph, a 747 would "dip" **~2.5 ft/min** to follow curvature—**undetectable** without instruments.  
  - Autopilot systems handle this via **barometric pressure** and **GPS altitude**.  

#### **C. Visual Proof**  
- **Long-Haul Flights**:  
  - A NYC-to-Tokyo flight (~6,700 miles) would require **~2,800 miles of "drop"** if Earth were flat.  
  - In reality, planes maintain **constant altitude** (e.g., 35,000 ft) without drastic pitching.  

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### **3. Why the Nose Isn’t Pulled Down Unevenly**  
- **Myth**: "Gravity pulls the nose down but not the tail."  
  - **Truth**: Gravity acts on the **entire plane uniformly**.  
  - Any imbalance would require **torque** (a rotational force), but:  
    - The plane’s **center of mass** and **lift distribution** prevent this.  
    - Control surfaces (elevators) keep the plane level.  

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### **4. Flat Earth Inconsistencies**  
- **Problem 1**: If Earth were flat, a plane flying "straight" would **gain altitude indefinitely** (no curvature to follow).  
- **Problem 2**: Gravity on a flat Earth would **not** pull "down" uniformly—it would require an unexplained force.  
- **Problem 3**: Celestial navigation (e.g., Polaris) **only works** on a spherical Earth.  

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### **5. Pilot Verification**  
- **Testimony**: Every commercial pilot is trained in **great-circle navigation**, which assumes curvature.  
- **Instrumentation**:  
  - **Attitude Indicator**: Shows aircraft orientation relative to the **horizon** (which curves).  
  - **Gyroscopes**: Align with Earth’s rotation (impossible on a flat plane).  

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### **Conclusion**  
Planes don’t "dip" to follow curvature because:  
1. Gravity pulls the **entire plane** uniformly (no uneven force on the nose).  
2. Lift automatically adjusts for the **gentle curve** (8" per mile² is irrelevant at flight scales).  
3. Flat Earth models **cannot explain** how planes maintain altitude without gaining height indefinitely.  

For deeper study:  
- FAA’s *Aeronautical Information Manual*: [https://www.faa.gov](https://www.faa.gov)  
- NASA’s curvature calculations: [https://spaceplace.nasa.gov](https://spaceplace.nasa.gov)  

Let me know if you’d like the **math for flight dynamics** or **flat Earth gravity models**!