Offensive Heat Transfer in the Middle Ages

Brady AydelotteSpencer Harding

Pre-launch AssumptionsTo=1120K

120lb draw weight

•The surface of the arrow had sufficient time to come to the adiabatic flame temperature of the residual fuel oil•The surface of the arrow was burned away, leaving only a uniform coating of carbon•Modern compound bows have arrow speeds of approximately 100 m/s for 65lbs of draw weight. Medieval compound bows had draw weights in excess of 120lbs. We assumed a velocity of 100 m/s for our arrow.

In-flight Assumptions•Time = 3.5 seconds

•Distance = 250 meters

•X-Velocity = 71m/s

•Arrow velocity is much greater than flame velocity so the flame on the arrow goes out immediately•The effect of radiation and convection were combined into a convective coefficient•The Whitaker correlation (eq 7.56) for spheres is still valid for Re# above 8e4

Assume spherical tip

EquationsRadiation:

Convection:

Lumped Capacitance:

Results

Straw: Ti = 580 K

Wood: Ti = 610 K

The final temperature, 1070 K is much greater than the ignition temperatures of wood and straw (610 and 580 K respectively) common building materials of the day.

Tf = 1070 K

Conclusion

• Medieval flaming arrows would be capable of igniting wooden and straw thatched structures even when the flame on the end went out.

References•Flame Structure and Processes, R.M. Fristrom, Oxford university Press, 1995

•http://www.engineeringtoolbox.com/fuels-ignition-temperatures-d_171.html

•http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V3B-47D05P2-2&_user=456938&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000021830&_version=1&_urlVersion=0&_userid=456938&md5=c2f18d43d39f4b7051f3489c022f65c4

•http://www.economy-point.org/i/ignition-temperature.html

•The Great Warbow: From Hastings to the Mary Rose (Hardcover). Matthew Strickland. Sutton Publishing 2005. ISBN-10: 0750931671, ISBN-13: 978-0750931670

•Fuels and Engines: Technology, Energy, Environment  By Jean-Claude Guibet, Emmanuelle Faure-Birchem