Piper Arrow Weight and Balance Calculator

Ensure Safe Flight Operations by Accurately Calculating Your Aircraft's Weight and Balance.

Aircraft Loading and Balance Calculation

Fuel Load

Payload (Baggage & Occupants)

Weight & Balance Envelope Chart

Visual representation of current weight and CG relative to the aircraft's approved envelope.

Detailed Load Breakdown

Item	Weight (lbs)	Arm (in)	Moment (in-lbs)
Aircraft Empty Weight	N/A	N/A	N/A
Fuel	N/A	N/A	N/A
Front Seat Occupants	N/A	N/A	N/A
Rear Seat Occupants	N/A	N/A	N/A
Baggage Area 1	N/A	N/A	N/A
Baggage Area 2	N/A	N/A	N/A
TOTALS	N/A		N/A

Detailed breakdown of each loaded item, its contribution to weight, and its moment.

What is Piper Arrow Weight and Balance?

The Piper Arrow Weight and Balance calculation is a critical pre-flight procedure that determines the aircraft's total weight and the location of its center of gravity (CG) relative to its structural and aerodynamic limits. In simple terms, it ensures the aircraft is not too heavy to fly and that its weight is distributed correctly for stable and controlled flight. For a specific aircraft like the Piper Arrow, this involves understanding its empty weight, the weight of fuel and payload (occupants and baggage), and how these components contribute to the overall CG. This calculation is not just a recommendation; it's a mandatory safety requirement mandated by aviation authorities worldwide.

Who should use it?

Every pilot operating a Piper Arrow (or any aircraft) is required to perform a weight and balance calculation before each flight. This includes:

• Certified Flight Instructors (CFIs)
• Private Pilot License (PPL) holders
• Commercial Pilot License (CPL) holders
• Airline Transport Pilot License (ATPL) holders
• Students undertaking flight training
• Aircraft owners and operators

Essentially, anyone responsible for the safe operation of the aircraft needs to understand and execute this process. It's fundamental to safe aviation practices.

Common Misconceptions:

• "It's just for heavy cargo planes": Weight and balance is crucial for all aircraft, from small singles like the Piper Arrow to large airliners.
• "My POH has the limits, so I don't need to calculate": The POH (Pilot's Operating Handbook) or AFM (Aircraft Flight Manual) provides the limits, but you MUST calculate your specific loaded condition to ensure you are within those limits.
• "It's too complicated for me": With modern calculators and clear procedures, it's more accessible than ever. Understanding the basics is key.

Piper Arrow Weight and Balance Formula and Mathematical Explanation

The core of weight and balance calculation lies in two fundamental principles: total weight and the center of gravity (CG). Every item loaded onto the aircraft contributes to the total weight, and each item also has a 'moment' which affects the CG. A moment is calculated by multiplying the weight of an item by its horizontal distance from a reference datum (usually the aircraft's nose or wing leading edge). The sum of all moments, divided by the total weight, gives the aircraft's CG.

The Piper Arrow, like other aircraft, has specific reference points and weight/CG limits defined in its official documentation (POH/AFM). These limits are essential for ensuring the aircraft remains stable and controllable throughout its flight envelope.

Step-by-Step Derivation:

1. Calculate the Weight of Each Component: Determine the weight of the aircraft empty, fuel, occupants, and baggage.
2. Determine the Arm of Each Component: Find the horizontal distance (arm) of each component's CG from the aircraft's reference datum. This is often provided in the POH/AFM, typically in inches or millimeters.
3. Calculate the Moment for Each Component: Multiply the weight of each component by its arm: Moment = Weight × Arm.
4. Sum All Weights: Add up the weights of all components to get the Total Weight.
5. Sum All Moments: Add up all the individual moments to get the Total Moment.
6. Calculate the Aircraft's CG: Divide the Total Moment by the Total Weight: CG = Total Moment / Total Weight.
7. Convert CG to MAC % (if necessary): The calculated CG is usually in inches or millimeters from the datum. This needs to be converted into a percentage of the Mean Aerodynamic Chord (MAC). The formula for this conversion is provided in the aircraft's POH/AFM, and typically looks like: CG (MAC %) = [(Aircraft CG (in) - Forward CG Limit (in)) / MAC (in)] × 100. Our calculator often simplifies this by taking direct CG values (like MAC %) as input or output.
8. Compare to Limits: Ensure the Total Weight is below the maximum allowable takeoff weight, and the calculated CG (in MAC %) falls within the approved forward and aft CG limits for the given weight.

Variable Explanations:

Variable	Meaning	Unit	Typical Range (Piper Arrow)
Empty Weight	The weight of the aircraft itself, including fixed equipment, but excluding unusable fuel, crew, baggage, and usable fuel.	lbs	1400 – 1650 lbs
Empty Weight CG	The center of gravity location of the aircraft in its empty configuration, expressed as a percentage of the Mean Aerodynamic Chord (MAC).	MAC %	15% – 35% (approximate, varies by model)
Useful Load	The maximum weight of the pilot, passengers, baggage, usable fuel, and drainable oil.	lbs	800 – 1000 lbs (approximate, varies by model and configuration)
Fuel Weight	The weight of the usable fuel onboard.	lbs	0 – ~440 lbs (for 72 gal)
Fuel Weight per Gallon	The density of the fuel being used.	lbs/gal	~5.8 (Jet A) to ~6.1 (Avg. High Octane)
Occupant Weight	The combined weight of pilot, co-pilot, and passengers.	lbs	0 – ~400 lbs per seat (subject to max useful load)
Baggage Weight	The weight of baggage carried in designated compartments.	lbs	0 – ~200 lbs (subject to compartment limits and max useful load)
Arm	The horizontal distance from the aircraft's reference datum to the CG of an item.	inches	Varies significantly; typically -20 to 150+ inches for Piper Arrow.
Moment	The product of an item's weight and its arm (Weight x Arm).	inch-lbs	Calculated value.
Total Weight	The sum of all weights (empty, fuel, payload).	lbs	Must be below Max Takeoff Weight (e.g., 2550 lbs for PA-28R-201).
Total Moment	The sum of all moments.	inch-lbs	Calculated value.
Center of Gravity (CG)	The calculated point where the aircraft's weight is balanced. Expressed as MAC %.	MAC %	Must be within the published limits for the specific weight (e.g., 20% – 30% for PA-28R-201 at MTOW).

Practical Examples (Real-World Use Cases)

Let's walk through two scenarios for a Piper Arrow PA-28R-201 T-Arrow, which has an Empty Weight of 1550 lbs, an Empty Weight CG of 28% MAC, a Useful Load of 950 lbs, and a Max Takeoff Weight of 2550 lbs. The approved CG range at 2550 lbs is 20% to 30% MAC.

Example 1: Solo Cross-Country Trip with Light Baggage

Scenario: A pilot is flying solo with a moderate amount of baggage for a cross-country flight. They are carrying 60 gallons of fuel.

Inputs:

• Aircraft Empty Weight: 1550 lbs
• Empty Weight CG: 28% MAC
• Useful Load: 950 lbs
• Fuel Weight per Gallon: 6.0 lbs/gal
• Fuel Gallons: 60 gal
• Front Seat Occupants: 180 lbs
• Rear Seat Occupants: 0 lbs
• Baggage Area 1: 60 lbs
• Baggage Area 2: 0 lbs

Calculation:

• Fuel Weight: 60 gal * 6.0 lbs/gal = 360 lbs
• Total Payload Weight: 180 (pilot) + 0 (rear) + 60 (baggage 1) = 240 lbs
• Total Weight: 1550 (empty) + 360 (fuel) + 240 (payload) = 2150 lbs
• *Note: This is well below the Max Takeoff Weight of 2550 lbs.*
• (Using typical arms for Piper Arrow PA-28R-201: Empty Wt CG 28% MAC, Fuel 360 lbs at 48″, Pilot 180 lbs at 40″, Baggage 1 60 lbs at 95″)
• Total Moment: (1550 * 28%) + (360 * 48″) + (180 * 40″) + (60 * 95″) = 4340 (moment from empty CG) + 17280 + 7200 + 5700 = 34520 inch-lbs
• CG Calculation: 34520 inch-lbs / 2150 lbs = 16.06 inches from Datum.
• To convert to MAC % (assuming datum at -141.1 inches and MAC at 50 inches for PA-28R-201): CG (MAC %) = [(16.06 – (-141.1)) / 50] * 100 = [(157.16) / 50] * 100 = 314.32% MAC.
• *Correction needed for common calculator inputs. If the calculator takes direct MAC % for empty weight, we calculate the loaded CG MAC % directly.*
• Using calculator logic that sums moments based on input MAC % and arm relationships:
• Total Weight = 2150 lbs
• Total Moment (using simplified calculation based on average arm for each item type): (1550 * 0.28) + (360 * 0.48) + (180 * 0.40) + (60 * 0.95) = 434 (moment units from EW CG) + 172.8 + 72 + 57 = 735.8 (moment units).
• CG (MAC %): 735.8 / 2150 = 0.3422 or 34.22% MAC.
• Interpretation: The total weight (2150 lbs) is within limits. However, the calculated CG (34.22% MAC) is FORWARD of the typical Piper Arrow envelope (e.g., 20-30% MAC at this weight). This load distribution is NOT safe. The pilot would need to reposition weight aft (e.g., move baggage to area 2 if available and allowed, or reduce front seat weight if possible) or reduce fuel/payload.

Example 2: Full Load with Two Passengers and Max Baggage

Scenario: Four adults are flying, and they are carrying the maximum allowable baggage in Area 1.

Inputs:

• Aircraft Empty Weight: 1550 lbs
• Empty Weight CG: 28% MAC
• Useful Load: 950 lbs
• Fuel Weight per Gallon: 6.0 lbs/gal
• Fuel Gallons: 72 gal (full tanks)
• Front Seat Occupants: 360 lbs
• Rear Seat Occupants: 340 lbs
• Baggage Area 1: 120 lbs (assuming this is within limits for the POH)
• Baggage Area 2: 0 lbs

Calculation:

• Fuel Weight: 72 gal * 6.0 lbs/gal = 432 lbs
• Total Payload Weight: 360 (front) + 340 (rear) + 120 (baggage 1) = 820 lbs
• Total Weight: 1550 (empty) + 432 (fuel) + 820 (payload) = 2802 lbs
• *Check against Useful Load: 820 lbs payload + 432 lbs fuel = 1252 lbs. This exceeds the Useful Load of 950 lbs.*
• Interpretation: This loadout is NOT possible. The total weight (2802 lbs) also exceeds the Maximum Takeoff Weight of 2550 lbs. The pilot must reduce the load. For instance, they might need to carry less fuel (e.g., 48 gallons = 288 lbs fuel) and potentially reduce passenger weight or baggage to stay within the useful load and maximum takeoff weight. If they reduced fuel to 48 gallons (288 lbs) and kept the passengers/baggage, the Total Weight would be 1550 + 288 + 820 = 2658 lbs. This is still over MTOW. They would need to adjust passenger weight or baggage further.

How to Use This Piper Arrow Weight and Balance Calculator

Our calculator is designed to simplify the pre-flight weight and balance check for your Piper Arrow. Follow these steps for accurate results:

1. Gather Aircraft Data: Locate your Piper Arrow's Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM). You'll need the Aircraft Empty Weight, Empty Weight Center of Gravity (CG), Useful Load, and Maximum Takeoff Weight.
2. Determine Payload Weights: Accurately estimate the weight of all occupants (pilot, passengers) and any baggage you plan to carry. Ensure these weights are realistic.
3. Determine Fuel Load: Note the total gallons of usable fuel you intend to carry. Select the appropriate fuel density (lbs/gal) based on the fuel type.
4. Enter Data into Calculator: Input the values from steps 1, 2, and 3 into the corresponding fields in the calculator above.
5. Calculate: Click the "Calculate Balance" button.
6. Review Results:
   • Primary Result: The "Balance Status" will clearly indicate if your aircraft is within the weight and CG limits ("In Limits", "Overweight", "Out of CG Envelope").
   • Intermediate Values: Check the "Current Weight", "Current CG", and "Total Moment" for detailed figures.
   • Assumptions: Verify that key parameters like Max Useful Load and Envelope Max Weight match your aircraft's specifications.
   • Detailed Breakdown: The table shows how each item contributes to the total weight and moment.
   • Chart: The visual chart plots your current loading against the aircraft's approved envelope, offering an immediate understanding of your status.
7. Decision Making: If the results indicate your aircraft is out of limits (either overweight or outside the CG envelope), you must adjust the load. This may involve removing baggage, reducing fuel, or having lighter occupants. Re-calculate after making adjustments until all parameters are within the green (In Limits).
8. Resetting: To start fresh or clear previous entries, click the "Reset Defaults" button.
9. Copying: The "Copy Results" button allows you to easily transfer the calculated summary, key assumptions, and status to a document or notes.

Key Factors That Affect Piper Arrow Weight and Balance Results

Several factors significantly influence the weight and balance calculation for your Piper Arrow. Understanding these can help you manage your aircraft's loading more effectively:

1. Aircraft Empty Weight and CG: This is the baseline. Any variations from the standard empty weight (e.g., due to installed optional equipment or recent maintenance) will shift the empty weight CG and require recalculation. This is why accurate weighing is important.
2. Fuel Load: Fuel is often the most variable component of weight and CG. Full tanks move the CG forward, while near-empty tanks move it aft. The weight of fuel also significantly impacts the total weight.
3. Occupant Weight and Seating Position: The weight of the pilot and passengers is a major payload factor. Furthermore, where they sit matters. Front-seat occupants typically have an arm closer to the datum (moment further forward), while rear-seat occupants have a more aft arm (moment further aft).
4. Baggage Weight and Location: Different baggage compartments have different arms. Placing heavier items in compartments with more aft arms will shift the CG aft. Always adhere to the specific weight limits for each compartment.
5. Optional Equipment and Modifications: Installing new avionics, interior modifications, or structural changes can alter the aircraft's empty weight and CG. These must be properly documented and factored into the weight and balance calculations.
6. Usable vs. Unusable Fuel: The POH specifies usable fuel. While unusable fuel is part of the aircraft's empty weight, it's critical to only calculate with the *usable* fuel you intend to carry.
7. Maintenance and Repairs: Major maintenance actions, like replacing heavy components or adding reinforcing structures, can change the aircraft's empty weight and CG.
8. "Draining" Oil: While often overlooked, the weight of engine oil is part of the useful load calculation. A full oil change adds significant weight compared to a minimum quantity.

Frequently Asked Questions (FAQ)

Q: What is the Mean Aerodynamic Chord (MAC)?

A: The MAC is the average chord length of the wing. CG is often expressed as a percentage of the MAC (MAC %) because it provides a standardized reference point for the aircraft's center of lift, regardless of the wing's varying chord length. The forward and aft limits are expressed in MAC % in the POH.

Q: How often does the weight and balance need to be recalculated?

A: It needs to be recalculated anytime the aircraft's empty weight or empty weight CG changes, or when the loading configuration (fuel, payload) is different from previous calculations. For routine operations, you perform it before each flight.

Q: What happens if I fly outside the CG limits?

A: Flying outside the CG limits can lead to serious controllability issues. If too far forward, the aircraft may be nose-heavy and difficult to rotate for takeoff or keep trimmed. If too far aft, it may be unstable, have a tendency to pitch up, and be difficult to recover from stalls or unusual attitudes.

Q: How do I find my aircraft's specific CG limits?

A: Your Piper Arrow's Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM) contains a detailed Weight & Balance section, including the approved CG range for various weights.

Q: Can I use a different fuel weight per gallon?

A: Yes, you can select the most appropriate fuel weight per gallon based on the type of fuel you are using (e.g., Avgas 100LL is about 6.0 lbs/gal, Jet A is about 5.8 lbs/gal). Using an incorrect density can lead to calculation errors.

Q: What is the difference between useful load and payload?

A: Useful load is the total weight available for crew, passengers, baggage, and usable fuel. Payload is typically defined as the weight of passengers and baggage only. So, Useful Load = Payload + Fuel.

Q: My empty weight CG is different from the POH, what should I do?

A: If you have installed equipment or made modifications that alter the empty weight and CG, you must have the aircraft re-weighed and a new Weight & Balance computation (often called a Schedule of Equipment List) created and entered into the aircraft records. Use these updated figures.

Q: Does this calculator account for taxi, takeoff, and landing phases?

A: This calculator provides a snapshot of the aircraft's weight and balance at a specific point in time (typically for takeoff). As fuel burns off during flight, the total weight decreases, and the CG typically shifts aft. Pilots should consider the CG at the end of the flight as well, especially for longer flights.