What makes your Dream fly further -Study on factors influencing the paper plane flight distance and time Group member: Chen Simiao, Liu Bin, Yu Weiwei, Bian Zuoer, Zhao Qinhao

Background Every boy and girl dreamt about a paper plane would never fall Paper plane flying is also a competitive sport Austrian paper airplane world championships World record 58.82m,1985 27.6s,1998

literature review Almost No academic literature Mostly from high school student study some topics: The distance has nothing to do with the size of plane(《如何使纸飞机飞得更远探究试验报告》) Gravity centre position has a linear relation on flight distance（李忡壕等《我要高飞》）

Response & controlled variables Response variable Flight time Flight distance Controlled variables 控制变量（单位） 正常水平与可操作范围 起飞角度 0°45° 机身长宽比 0.5,1.0,1.5 机翼宽度 18cm,15cm,12cm 纸张厚薄度 普通A4纸，普通牛皮纸 机翼仰角 45°90°120° 重心位置 1/3,1/2,2/3 飞机头形状 尖头 平头 尾翼 无尾翼 有尾翼 侧翼 无侧翼 有侧翼 控制变量（单位） 正常水平与可操作范围 测量精度与方法 推荐试验设置 对响应变量的预期效果 起飞角度 0°45° 精确测量到度 飞机起飞设备 0°可能会使飞行距离更远 纸张厚薄度 普通A4纸，普通牛皮纸 牛皮纸可能会使飞行距离更远 机翼仰角 90°120° 90°可能会使飞行距离更远 重心位置 1/3,1/2 估测 1/3可能会使飞行距离更远 尾翼 无尾翼 有尾翼 无尾翼可能会使飞行距离更远 侧翼 无侧翼 有侧翼 有侧翼可能会使飞行距离更远

Preliminary experiment design 设计生成元: E = ABC, F = BCD 定义关系:I = ABCE = BCDF = ADEF 别名结构 I + ABCE + ADEF + BCDF A + BCE + DEF + ABCDF B + ACE + CDF + ABDEF C + ABE + BDF + ACDEF D + AEF + BCF + ABCDE E + ABC + ADF + BCDEF F + ADE + BCD + ABCEF AB + CE + ACDF + BDEF AC + BE + ABDF + CDEF AD + EF + ABCF + BCDE AE + BC + DF + ABCDEF AF + DE + ABCD + BCEF BD + CF + ABEF + ACDE BF + CD + ABDE + ACEF ABD + ACF + BEF + CDE ABF + ACD + BDE + CEF Factorial design Replication = 2 No block(=1) No center points Randomize Definition relationship 定义关系:I = ABCE = BCDF = ADEF

Experiment conduction

Experiment conduction(cont) ½ gravity control position 1/3 gravity control position With empennage With flank

Data analysis for preliminary experiment

Data analysis for preliminary experiment(cont)

Conclusion form preliminary experiment For flight distance There are 4 first order factors: Gravity center position, paper type, fly angle, empennage(侧翼) For flight time There is 1 first order factors: fly angle fly angle*paper type We only need to keep 4 factors in later experiment

Later experiment design—set parameters

Data analysis (1)

Interaction analysis

Data analysis (3)

Model developing Y=3.15844-0.020937*A+0.760312*B-0.894062*C-0.134062*D-0.374062*A*B-0.470938*B*C*D 取值/因素 起飞角度A 纸张类型B 重心位置C 有无侧翼D -1 打印纸 1/3 无侧翼 1 45 卡纸 1/2 有侧翼

Model developing Y=1.05938-0.015625*A+0.103125*B+0.128125*D-0.153125*B*D+0.109375*A*B*D 取值/因素 起飞角度A 纸张类型B 重心位置C 有无侧翼D -1 打印纸 1/3 无侧翼 1 45 卡纸 1/2 有侧翼

Conclusion

Tips on folding a NB plane Gravity center should be as forward as possible Use high quality type paper for further distance Lighter paper for long flight time Fly at a 0°position Fold flank For convenience consideration don’t need empennage Angle between wings and main body should be 90° although it’s not significant

Thank you

Q & A