Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Vertical Rocket

垂直火箭

Develop expressions

推导表达式

Under the influence of the rocket thrust and gravity, the rocket velocity can be calculated as follows:

For exhaust velocity u = m/s
and burn rate dM/dt = kg/s
the rocket thrust is x10^ N.
For rocket mass = kg
and fuel mass = kg, the time of burn
is seconds and the velocity at burnout is calculated from

which gives vburnout = m/s.
在火箭推力和重力的影响下，火箭的速度可以这样计算：对于喷气速度 u = m/s 和燃烧率 dM/dt = kg/s，火箭推力为 x10^ N。对于火箭质量 = kg 和燃料质量 = kg，燃烧时间是秒，燃烧结束时的速度由上述计算得出，得到燃烧结束时的速度 v burnout = m/s。
中文译文中的待填/计算数值依次对应：1：u 2：br 3：fb 4：fp 5：mr 6：mf 7：tb 8：vb。实际数值以上方原输入框为准。
Fowles and Cassiday give as example data for a satellite launch a low orbit velocity of about 8 km/s, an initial velocity of about 0.5 km/s from the rotation of the earth near the equator, and an exhaust velocity of 2.5 km/s. You could use this data above to confirm that you could get only about 5 percent of the total initial mass into orbit. They suggest that effective ejection speeds for most rocket fuels are on the order of 2 to 4 km/s.
Fowles 和 Cassiday 给出一个卫星发射的例子数据：近地轨道的速度约为 8 km/s，地球赤道附近由于地球自转带来的初始速度约为 0.5 km/s，推进剂的喷射速度约为 2.5 km/s。你可以利用上述数据确认，仅能将总初始质量的约 5% 带入轨道。他们指出，大多数火箭燃料的有效喷射速度通常在 2 到 4 km/s 的范围内。
 Index

Rocket propulsion
索引 火箭推进
 
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