Sleeping Bag Comparison

Which sleeping bag will keep you warmer?

By: Kyle Layton and Ben Salazar

Introduction

• Camping is fun, but can be cold, especially in the winter.

• Many companies make claims that their brand of sleeping bag is better at keeping you warm in cold conditions

Research Objective:

• We want to compare two sleeping bags that have very similar materials and specifications but drastically different prices and experimentally find out which is more effective at retaining heat

• We will do this by deriving a heat transfer rate for the different forms of heat loss

• We will then plug in values for each sleeping bag that we measure in our experiment and obtain the heat transfer associated with each sleeping bag

• We will compare these values and determine which brand of sleeping bag is better at keeping a camper warm

Introduction – sleeping bags

• Sleeping bag 1 – Ledge Mummy Sleeping bag

• Operating temperatures: + 20º F

• Price: $60.00

• Sleeping bag 1 - Northface Mummy Sleeping bag

• Operating temperatures: + 20º F

• Price: $200.00

Which is better?

Materials used: •2 Small Zip-Loc bags large enough to fit 500 ml of liquid•Beaker•Water •Microwave •Two sleeping bags of the same size and style, but different brands•Infrared thermal laser digital thermometer •FLIR E5 compact thermal imaging infrared camera

Assumptions: •Zip Loc bags have uniform surface temperature •Zip Loc bags can be approximated as as spheres with properties of water •Sleeping bags can be approximated as flat surfaces •Floor can be treated as a semi-infinite solid•Thickness of material of sleeping bag can be neglected due to compression•1-D heat transfer

Methods

Methods

• Filled Zip-Loc bags with a fixed volume of warm water

• Measured water volume using a beaker: 475 ml = 475 x 10-6 m3

• Heated water to 49º C using a microwave

• Measured the temperature of water, the room, and the sleeping bag using an infrared thermal laser digital thermometer

• Placed Zip-Loc bags in sleeping bags and monitored temperature of both the sleeping bag and the Zip-Loc bag over a 45 min time interval.

• Took thermal images using FLIR E5 Compact Thermal Imaging InfraRed Camera for visualization purposes

• The bag of water at 49º C is assumed to heat at least a small portion of the sleeping bag. • If we approximate the patch of sleeping bag that was heated as a small plate we can use

the following equations:

• Using these values, the Rayleigh number was calculated for each corresponding measurement: Ra = Pr(Gr)

• This gave us a way to calculate the average h value for surfaces• Then, using the equation Qair = hA(ΔT*t), we calculated the heat transfer between each

measurement through free convection.• The total heat loss through the air was found by summing values for these Qair values( see

appendix)

Methods

• Heat transfer through the ground was calculated assuming a semi-infinite solid in contact with a uniform temperature surface, using:

• For each measurement, similar to the procedure outlined for Qair, q” values for each time interval were calculated and then summed

• Heat loss through the air (Qair ) and through the ground (q”) were then summed to determine the total heat loss

Methods

Results – Thermal images

Sleeping bag 1 – Ledge Mummy sleeping bag

Qtotal = 8970 W/m2

Results – Thermal Images

Sleeping bag 2 – Northface Mummy sleeping bag

Qtotal = 7890 W/m2

Conclusion

• A slight difference was detected between the two sleeping bag brands

• At Qtotal = 7890 Sleeping bag 2 more effectively retained heat and thus would keep a camper warmer

• This represents a 12% better heat retention

• Despite its better performance, we do not believe this justifies the $140 price difference between the two products

• We therefore recommend the use and purchase of the less expensive and still effective sleeping bag

Appendix – Experimental Measurements

Ledge

Time 0 min 5 min 10 min 15 min 20 min 25 min 30 min 35 min 40 min 45 min

Ts 26 32 30.3 28.5 29 28.5 27.5 28 27.5 27.5

Ts Kelvin 299.15 305.15 303.45 301.65 302.15 301.65 300.65 301.15 300.65 300.65

Northface

Time 0 min 5 min 10 min 15 min 20 min 25 min 30 min 35 min 40 min 45 min

Ts 27 28 28.5 28.8 29 27.5 27.5 27 28.5 26

Ts Kelvin 300.15 301.15 301.65 301.95 302.15 300.65 300.65 300.15 301.65 299.15

Appendix – Preliminary Calculations

Ledge Northface

Gr 483172.173 Ra 341119.554 Gr 603965.22 Ra 426399.44

1207930.43 852798.886 724758.26 511679.33

1002582.26 707823.075 785154.78 554319.28

785154.781 554319.276 821392.69 579903.24

845551.303 596959.22 845551.3 596959.22

785154.781 554319.276 664361.74 469039.39

664361.738 469039.387 664361.74 469039.39

724758.26 511679.331 603965.22 426399.44

664361.738 469039.387 785154.78 554319.28

664361.738 469039.387 483172.17 341119.55

h 3.52358034 Nu 13.0502975 h 3.7257326 Nu 13.79901

4.43066771 16.4098804 3.8994827 14.442528

4.22900991 15.6629997 3.9782999 14.734444

3.9782999 14.7344441 4.0234296 14.901591

4.05269285 15.0099735 4.0526928 15.009974

3.9782999 14.7344441 3.8155738 14.131755

3.81557375 14.1317546 3.8155738 14.131755

3.89948265 14.4425283 3.7257326 13.79901

3.81557375 14.1317546 3.9782999 14.734444

3.81557375 14.1317546 3.5235803 13.050298

Appendix – Final Calculations & Results

Ledge Northface

Q_air 2449.899329 Q_air 2112.714065

Q_floor 6519.085264 Q_floor 5774.654646Q_total 8968.984593 Q_total 7887.368711