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Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
 | This article relies on a single source. (October 2019) |
| Manufacturer | TRW and McDonnell Douglas |
|---|---|
| Country of origin | United States |
| Used on | Delta 1000 Delta 2000 Delta 3000 |
| General characteristics | |
| Height | 5.9 m (19 ft)[1] |
| Diameter | 2.4 m (7.9 ft)[1] |
| Gross mass | 6,954 kg (15,331 lb)[1] |
| Engine details | |
| Powered by | 1 TR-201 |
| Maximum thrust | 43.63 kN (9,810 lbf)[1] |
| Specific impulse | 319 seconds (3.13 km/s)[1] |
| Burn time | 431 seconds[1] |
| Propellant | Aerozine 50 / N2O4 |
The Delta-P is an American rocket stage, developed by McDonnell Douglas and TRW, first used on November 10, 1972 as the second stage for the Delta 1000 series. It continued to serve as the second stage for subsequent Delta 2000 and Delta 3000 flights for 17 years, with its last usage on February 8, 1988. It is propelled by a single TRW TR-201 rocket engine, fueled by Aerozine 50 and dinitrogen tetroxide,[1] which are hypergolic.
The Delta-P traces its heritage to the Apollo Lunar Module's Descent Propulsion System. The TR-201 engine is the Descent Propulsion System modified to be a fixed thrust engine.[2] The Descent Propulsion System was first fired in flight during the Apollo 5 mission, in a low Earth orbit test on January 22, 1968.
As the supply of these surplus Apollo engines was depleted, the Douglas/Aerojet Delta-K upper stage was introduced in the Delta 3000 program. The Delta-K was then exclusively used on the second stage for the Delta 4000, Delta 5000, and subsequent Delta II.
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The Delta-P is an American rocket stage, developed by McDonnell Douglas and TRW, first used on November 10, 1972 as the second stage for the Delta 1000 series. It continued to serve as the second stage for subsequent Delta 2000 and Delta 3000 flights for 17 years, with its last usage on February 8, 1988. It is propelled by a single TRW TR-201 rocket engine, fueled by Aerozine 50 and dinitrogen tetroxide, which are hypergolic. The Delta-P traces its heritage to the Apollo Lunar Module's Descent Propulsion System. The TR-201 engine is the Descent Propulsion System modified to be a fixed thrust engine. The Descent Propulsion System was first fired in flight during the Apollo 5 mission, in a low Earth orbit test on January 22, 1968. As the supply of these surplus Apollo engines was depleted, the Douglas/Aerojet Delta-K upper stage was introduced in the Delta 3000 program. The Delta-K was then exclusively used on the second stage for the Delta 4000, Delta 5000, and subsequent Delta II.
In structural engineering, the P-Δ or P-delta effect refers to the abrupt changes in ground shear, overturning moment, and/or the axial force distribution at the base of a sufficiently tall structure or structural component when it is subject to a critical lateral displacement. A distinction can be made between P-delta effects on a multi-tiered building, written as P-Δ, and the effects on members deflecting within a tier, written as P-δ. P-delta is a second-order effect on a structure which is loaded laterally. One first-order effect is the initial deflection of the structure in reaction to the lateral load. The magnitude of the P-delta effect depends on the magnitude of this initial deflection. P-delta is a moment found by multiplying the force due to the weight of the structure and applied axial load, P, by the first-order deflection, Δ or δ. NUMERICAL EXAMPLE OF P DELTA EFFECT ON A CALCULATOR You have a 1 meter tall rigid vertical rod that rotates on a hinge at the bottom of the rod. There is a 1 newton load on the top of the rod. The rod has a hinge with a rotational stiffness of 0.8 newton meters per radian of rotation. So you input any initial rotational angle on the rod. The following table shows that the rod will iterate to 1.13 radians where the rod will be in stable equilibrium. The formula for this table is next radians rotation=sin(last radians rotation)/.8 In the table from the formula you can see the rod starts at .1 radians and iterates to 1.13 radians where it is in stable equilibrium. .1 .124 .156 .194 .241 .300 .367 .448 .542 .645 .751 .853 .942 1.01 1.06 1.09 1.11 1.12 1.12 1.13 1.13 and so on as it converges to 1.13 radians where the rod is stable. The P DELTA effect finds the stable final deformed shape of a structure just like how the rod rotates to a final deformed position at 1.13 radians. The idea is that iteratively repeated linear structural analyses can solve a non linear structural analysis problem. It takes multiple iterations of a linear analysis to compute the final deformed shape of a structure where the P DELTA effect is significant. To illustrate the effect, consider a case in statics, a perfectly rigid body anchored on the ground subject to small lateral forces. In this example, a concentrated vertical load applied to the top of the structure and the weight of the structure itself are used to compute the ground reaction force and moment. Real structures are flexible and will bend to the side. The amount of bending is found through a strength of materials analysis. During this side displacement, the top has changed position and the structure is experiencing an additional moment, P×Δ, or near the middle, P×δ. This moment is not accounted for in a basic first-order analysis. By superposition, the structure responds to this moment by additional bending and displacement at the top. In some sense, the P-delta effect is similar to the buckling load of an elastic, small-scale solid column given the boundary conditions of a free end on top and a completely restrained end at the bottom, with the exception that there may exist an invariant vertical load at the top of the column. A rod planted firmly into the ground, given a constant cross-section, can only extend so far up before it buckles under its own weight; in this case the lateral displacement for the solid is an infinitesimal quantity governed by Euler buckling. If the lateral displacement and/or the vertical axial loads through the structure are significant then a P-delta analysis should be performed to account for the non-linearities.
P-Valley is an American drama television series created by Katori Hall. The series is an adaptation of Hall's play Pussy Valley, and follows primarily women working at a strip club in the Mississippi Delta. P-Valley stars Brandee Evans, Nicco Annan, J. Alphonse Nicholson, and Elarica Johnson. It premiered on Starz on July 12, 2020, and was renewed for a second season two weeks after its premiere. The second season premiered on June 3, 2022. In October 2022, the series was renewed for a third season. In September 2026, it was announced that the third season would be the last. The 9-episode final season is set to premiere with two episodes on December 4, 2026. P-Valley has received critical acclaim and garnered nominations from the GLAAD Media Awards, Independent Spirit Awards, TCA Awards, and the NAACP Image Awards.
The Laplace pressure is the pressure difference between the inside and the outside of a curved surface that forms the boundary between two fluid regions. The pressure difference is caused by the surface tension of the interface between liquid and gas, or between two immiscible liquids. The Laplace pressure is determined from the Young–Laplace equation given as Δ P ≡ P inside − P outside = γ ( 1 R 1 + 1 R 2 ) , {\displaystyle \Delta P\equiv P_{\text{inside}}-P_{\text{outside}}=\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right),} where R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} are the principal radii of curvature and γ {\displaystyle \gamma } (also denoted as σ {\displaystyle \sigma } ) is the surface tension. Although signs for these values vary, sign convention usually dictates positive curvature when convex and negative when concave. The Laplace pressure is commonly used to determine the pressure difference in spherical shapes such as bubbles or droplets. In this case, R 1 {\displaystyle R_{1}} = R 2 {\displaystyle R_{2}} : Δ P = γ 2 R {\displaystyle \Delta P=\gamma {\frac {2}{R}}} For a gas bubble within a liquid, there is only one surface. For a gas bubble with a liquid wall, beyond which is again gas, there are two surfaces, each contributing to the total pressure difference. If the bubble is spherical and the outer radius differs from the inner radius by a small distance, R o = R i + d {\displaystyle R_{o}=R_{i}+d} , the difference in pressure between the outer and inner regions of gas is Δ P = Δ P i + Δ P o = 2 γ ( 1 R i + 1 R i + d ) = 4 γ R i ( 1 − 1 2 d R i + d ) ≈ 4 γ R i + O ( d ) . {\displaystyle \Delta P=\Delta P_{i}+\Delta P_{o}=2\gamma \left({\frac {1}{R_{i}}}+{\frac {1}{R_{i}+d}}\right)={\frac {4\gamma }{R_{i}}}\left(1-{\frac {1}{2}}{\frac {d}{R_{i}+d}}\right)\approx {\frac {4\gamma }{R_{i}}}+{\mathcal {O}}(d).}
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Madam C.J. Walker