# shelter: jacket: design



Objective: To build a smart winter jacket with a lithium battery and 320 cm of heating wire.

> Imagine an adult person who is wearing a normal jacket in a -10-celsius  winter. To make them feel warm, how many watts of energy should we add, so to speak, inside the jacket? This is the heat that is generated by this device.

To determine the required power for a smart jacket to maintain body temperature in a -10°C environment, here's a practical breakdown: 1. **Body Heat Loss**: An adult at rest loses about **100–150 watts** of heat in extremely cold conditions (-10°C). This is the baseline power needed to maintain body temperature. 2. **Jacket Efficiency**: A smart jacket with heating elements (like wires) is not 100% efficient. Assume **30–50% efficiency** for the system (due to losses in the heating elements, insulation, and materials). This means only a fraction of the input power becomes usable heat. 3. **Required Input Power**: To offset the 100–150 watts of heat loss, the jacket must input **more than that** to account for inefficiency. - At **30% efficiency**: $$ \text{Input Power} = \frac{100\ \text{W}}{0.3} \approx 333\ \text{W} $$ - At **50% efficiency**: $$ \text{Input Power} = \frac{100\ \text{W}}{0.5} = 200\ \text{W} $$ 4. **Practical Consideration**: You'll need a lithium battery capable of supplying **200–300 watts of continuous power**. However, real-world variables (e.g., jacket insulation, ambient wind, user activity) might increase this requirement. **Answer**: The jacket needs **approximately 200–350 watts of input power**, depending on efficiency and environmental factors.

🧠 query id: `watts`

> What is the nominal current that is drawn from the battery?

To calculate the **nominal current** drawn from the battery, we'll use the formula: $$ I = \frac{P}{V} $$ Where: - $ I $ = Current (in amperes) - $ P $ = Power (in watts) - $ V $ = Battery voltage ### Assumptions: - **Battery voltage**: A typical lithium-ion battery operates at **3.7 volts** (nominal voltage for a single cell). - **Power range**: From earlier, we determined the jacket requires **200–350 watts** of input power. ### Calculation: $$ I = \frac{200\ \text{W}}{3.7\ \text{V}} \approx 54\ \text{A} \quad \text{(for 200 W)} $$ $$ I = \frac{350\ \text{W}}{3.7\ \text{V}} \approx 94\ \text{A} \quad \text{(for 350 W)} $$ ### Result: The jacket would draw a **nominal current of 54–94 amperes**, depending on the power demand. ### Key Notes: 1. **Battery Capacity**: A lithium-ion battery rated for 3.7 volts must have sufficient **amp-hour (Ah)** capacity to sustain this current for the desired runtime. 2. **Voltage Fluctuations**: Real-world lithium batteries have a voltage range (e.g., 3.0 V to 4.2 V), so the current will vary slightly during discharge. 3. **Efficiency Impact**: If the heating system is less efficient (e.g., 30% efficiency), the actual power draw could be **higher** (e.g., closer to 94 A for 350 W). This calculation assumes a single-cell battery. For a multi-cell pack (e.g., 3.7 V × 3 cells = 11.1 V), the current would decrease proportionally (e.g., 54 A ÷ 3 ≈ 18 A for 200 W). Always verify with a battery datasheet for exact specs.

🧠 query id: `current`

> What is the resistance per meter of the heating wire?

To determine the **resistance per meter** of the heating wire, you need to know three key parameters: 1. **Resistivity (ρ)** of the wire material (e.g., nichrome, carbon fiber, etc.). 2. **Cross-sectional area (A)** of the wire. 3. **Length (L)** of the wire (though we’re calculating resistance per meter, so length cancels out). ### Formula: $$ \text{Resistance per meter} = \frac{\rho}{A} $$ Where: - $ \rho $ (rho) is the resistivity of the material (in ohm-meters, Ω·m). - $ A $ is the cross-sectional area of the wire (in square meters, m²). --- ### Step-by-Step Example: #### 1. **Choose a Material** Let’s assume you’re using **nichrome** (a common heating wire material). - **Resistivity of nichrome**: ~ $ 1.1 \times 10^{-6} \, \Omega \cdot \text{m} $. #### 2. **Determine Cross-Sectional Area** If the wire has a diameter of 0.5 mm (a typical size for heating wires), calculate the cross-sectional area: - **Diameter** $ d = 0.5 \, \text{mm} = 0.0005 \, \text{m} $. - **Radius** $ r = d/2 = 0.00025 \, \text{m} $. - **Area** $ A = \pi r^2 = \pi (0.00025)^2 \approx 1.96 \times 10^{-7} \, \text{m}^2 $. #### 3. **Calculate Resistance per Meter** $$ \text{Resistance per meter} = \frac{1.1 \times 10^{-6}}{1.96 \times 10^{-7}} \approx 5.6 \, \Omega/\text{m} $$ --- ### Practical Implications: - **Resistance per meter** tells you how much the wire opposes current flow per unit length. - For your 320 cm (3.2 m) heating wire, total resistance would be: $$ R_{\text{total}} = 5.6 \, \Omega/\text{m} \times 3.2 \, \text{m} \approx 18 \, \Omega $$. - This resistance, combined with the battery voltage, determines the current (via Ohm’s Law) and power consumption. --- ### Key Notes: 1. **Material Choice**: Nichrome has a high resistivity and is durable, but other materials (e.g., carbon fiber) may have different resistivity values. 2. **Wire Gauge**: Thicker wires (larger cross-sectional area) have lower resistance per meter. 3. **Accuracy**: Use precise measurements for diameter and material specifications to ensure reliability. If you share the wire material and dimensions, I can calculate the exact resistance per meter for your design!

🧠 query id: `resistance`

> If we use a battery-capacity::: li-ion battery, for how long can we keep this device on?

To determine how long a Li-ion battery can power your smart jacket, you need to know: 1. **Battery Capacity (Ah)**: Typically listed as "X amp-hours" (e.g., 2000 mAh or 2 Ah). 2. **Current Draw (A)**: The nominal current calculated earlier (54–94 A for your jacket). 3. **Efficiency and Real-World Factors**: Battery efficiency, heat losses, and usage patterns. ### Formula: $$ \text{Runtime (hours)} = \frac{\text{Battery Capacity (Ah)} \times \text{Battery Voltage (V)}}{\text{Power Consumption (W)}} $$ Or, simplified: $$ \text{Runtime} = \frac{\text{Battery Capacity (Ah)}}{\text{Current (A)}} $$ ### Example: Assume a **Li-ion battery** with: - **Capacity**: 2000 mAh (2 Ah) - **Voltage**: 3.7 V - **Current Draw**: 54 A (minimum case) #### Step 1: Convert Battery Capacity to Watt-hours (Wh) $$ \text{Wh} = \text{Ah} \times \text{V} = 2 \, \text{Ah} \times 3.7 \, \text{V} = 7.4 \, \text{Wh} $$ #### Step 2: Calculate Runtime If the jacket draws **200 W** (as calculated earlier), runtime is: $$ \text{Runtime} = \frac{7.4 \, \text{Wh}}{200 \, \text{W}} = 0.037 \, \text{hours} \approx 2.2 \, \text{minutes} $$ #### Step 3: Adjust for Real-World Factors - **Battery Efficiency**: Li-ion batteries are ~90% efficient. Multiply runtime by 0.9: $$ 2.2 \, \text{minutes} \times 0.9 = 2.0 \, \text{minutes} $$ - **Usage Patterns**: If the jacket is not constantly at maximum power (e.g., 50% of 200 W), runtime increases. ### Key Takeaways: 1. **Smaller Batteries**: A 2000 mAh battery (7.4 Wh) lasts only **a few minutes** under heavy load. 2. **Larger Batteries**: For longer runtime, use a **higher capacity battery** (e.g., 10,000 mAh or 37 Wh). 3. **Battery Voltage**: Higher voltage reduces current draw (e.g., a 11.1V battery at 54 A would draw ~4.8 A instead of 54 A). ### Practical Recommendation: To power a 200–350 W jacket for **1 hour**, you’d need a battery with: - **Minimum Capacity**: $$ \text{Wh} = 200 \, \text{W} \times 1 \, \text{hour} = 200 \, \text{Wh} $$ - A 3.7V battery: $ \frac{200}{3.7} \approx 54 \, \text{Ah} $ (e.g., a 54 Ah Li-ion pack). - A 11.1V battery: $ \frac{200}{11.1} \approx 18 \, \text{Ah} $. **Conclusion**: A standard Li-ion battery (e.g., 2000 mAh) is **not sufficient** for long-term use. You’ll need a **larger battery pack** (e.g., 10,000 mAh or higher) or a higher-voltage Li-ion system (e.g., 11.1V) to achieve practical runtime. Always account for inefficiencies and real-world conditions!

🧠 query id: `operation-time`

## build

```bash
@sbc build_README \
	ai,root=shelter/jacket/design

@upload public,zip jacket-design-v3
```

[jacket-design-v3.tar.gz](https://kamangir-public.s3.ir-thr-at1.arvanstorage.ir/jacket-design-v3.tar.gz)
