Page:EB1922 - Volume 30.djvu/428

388

TABLE I.

f 2

if

v*

p 2

1)2

v>

%

v*

IOO

log. G.

IOO

log. G.

IOO

log. G.

foo ,

log. G.

IOO

log. G.

IOO

log.G.

IOO

log. G.

IOO

log. G.

8000

9-5043

9000

9-5225

o

400

8-4354

800

8-7151

1 200

9-0661

1600

9-2282

2OOO

9-2974

6000

9-4655

IOOOO

9-5399

10

7.7244

410

8-4415

810

8-7238

1210

9-0727

1610

9-2306

2100

9-3093

6100

9-4676

IIOOO

9-5568

20

7-8655

420

8-4474

820

8-7328

I22O

9-0791

1620

9-2329

22OO

9-3.199

6200

9-4696

I2OOO

9'573i

30

7-9462

430

8-4534

830

8-7416

1230

9-0852

1630

9-2351

2300

9-3295

6300

9-4716

13000

9-5888

40

8-0025

440

8-4594

840

8-7506

1240

9-0912

1640

9-2373

2400

9-3381

6400

9-4736

14000

9-6034

50

8-0453

450

8-4654

850

8-7597

1250

9-0972

1650

9-2395

2500

9-3459

6500

9-4756

15000

9-6172

60

8-0800

460

8-4716

860

8-7688

I26O

9-1028

1660

9-2417

26OO

9-3531

6600

9-4776

16000

9-6304

70

8-1089

470

8-4776

870

8-7781

I27O

9-1083

1670

9-2438

2700

9-3598

6700

9-4796

17000

9-6429

80

8-1336

480

8-4836

880

8-7873

1280

9-II37

1680

9-2459

2800

6800

9-4815

18000

9-6549

90

8-I552

490

8-4899

890

8-7967

I29O

9-1189

1690

9-2479

29OO

9-37I5

6900

9-4835

19000

9-6662

IOO

8-1745

500

8-4959

900

8-8061

1300

9-1240

1700

9-2499

3000

9-3769

7000

9-4854

2OOOO

9-6769

no

8-1917

510

8-5021

910

8-8155

1310

9-1289

1710

9-2519

3100

9-3819

7100

9-4874

2IOOO

9-6873

I2O

8-2074

520

8-5084

920

8-8251

1320

9-1337

1720

9-2539

3200

9-3865

7200

9.4893

22OOO

9-6973

130

8-2217

530

8-5I47

930

8-8346

1330

9-1384

1730

9-2558

3300

9-3910

7300

9-4912

23OOO

9-7068

140

8-2349

540

8-5211

940

8-8442

1340

9-1430

1740

9-2576

3400

9-3951

7400

9-4931

24000

9-7159

150

8-2471

550

8-5275

950

8-8538

1350

9-1474

1750

9-2595

3500

9-3991

7500

9-4950

25OOO

9-7246

1 60

8-2586

560

8-5340

960

8-8633

1360

9-I5I7

1760

9-2613

3000

9-4029

7600

9-4969

26OOO

9-7331

170

8-2693

570

8-5405

970

8-8728

1370

9-1559

1770

9-1631

3700

9-4065

7700

9-4988

2-OOO

9-7412

1 80

8-2794

580

8-5472

980

8-8823

1380

9-1599

1780

9-2648

3800

9-4100

7800

9-5006

28OOO

9-7490

190

8-2891

590

8-5539

990

8-8919

1390

9-1639

1790

9-2665

3900

9-4I33

7900

9-5025

29OOO

9-7566

200

8-2982

600

8-5607

IOOO

8-9014

I4OO

9-1678

1800

9-2682

4OOO

9-4165

8000

9-5043

3OOOO

9-7639

2IO

8-3070

610

8-5676

IOIO

8-9107

1410

9-I7I5

1810

9-2699

4IOO

9-4196

31000

9-7710

22O

8-3I54

620

8-5745

IO2O

8-9200

I42O

9-I752

1820

9-2715

42OO

9-4226

32OOO

9-7779

230

8-3234

630

8-5816

1030

8-9293

H30

9-1788

1830

9-2731

4300

9-4254

240

8-3312

640

8-5887

1040

8-9385

1440

9-1822

1840

9-2747

44OO

9-4282

250

8-3388

650

8-5959

1050

8-9476

1450

9-I857

1850

9-2763

4500

9-4309

260

8-3461

660

8-6031

IO6O

8-9566

1460

9-1890

1860

9-2779

46OO

9-4335

27O

8-3531

670

8-6105

1070

8-9654

1470

9-1922

1870

9-2794

4700

9-4360

280

8-3601

680

8-6180

IO8O

8-9741

1480

9-1953

1880

9-2809

4800

9-4385

20X)

8-3668

690

8-6255

IOOX)

8-9826

1490

9-1984

1890

9-2824

4900

9-4410

300

8-3735

700

8-6332

IIOO

8-9910

1500

9-2014

1900

9-2838

5000

9-4434

310

8-3800

710

8-6409

IIIO

8-9994

1510

9-2044

1910

9-2853

5100

9-4458

320

8-3864

720

8-6488

II2O

9-0075

1520

9-2072

1920

9-2867

5200

9-4481

33

8-3928

730

8-6568

1130

9-oi53

1530

9-2100

1930

9-2881

5300

9-4504

34

8-3989

74

8-6648

II4O

9-0232

1540

9-2128

1940

9-2895

5400

9-4526

350

8-4051

750

8-6729

1150

9-0308

1550

9-2155

1950

9-2909

5500

9-4548

360

8-4113

760

8-681 i

II60

9-0382

1560

9-2182

1960

9-2922

5600

9-4570

370

8-4174

770

8-6895

1170

9-0454

1570

9-2207

1970

9-2935

5700

9-4592

380

8-4234

780

8-6960

1180

9-0524

1580

9-2232

1980

9-2948

5800

9-4613

390

8-4294

790

8-7065

1190

9-0594

1590

9-2257

1990

9-2961

5900

9-4634

400

8-4354

800

8-7151

1 200

9-0661

I6OO

9-2282

2OOO

9-2974

60OO

ences in air resistance between projectiles now used and those with which the air resistance law was determined. Its value. I for the projectiles of the form used in determining the air- resistance law, is as low as 0-47 for modern sharp-pointed, boat- tailed projectiles. Its value can be accurately determined for any projectile by working backward from the results of firing. Such determinations show that the value may and usually does vary for the same projectile if fired at different ranges. The Differential Equations of Motion of the. Projectile. Neglecting the convergence of the action lines of gravity due to the spheroidal form of the earth and also the slight diminution in the intensity of the force of gravity due to the height which modern projectiles reach, we may write the differential equations of motion of the projectile considered as a material point, as follows:

(4) g'= -Rcos0 = *"

FIG. 2.

where, (see fig. 2), x is the abscissa of any point of the trajectory, positive to the right,

x', the horizontal component of the velocity at that point,

x", the horizontal component of the acceleration,

y, the ordinate corresponding to x, positive up,

y', the vertical component of the velocity at that point,

y", the vertical component of the acceleration,

6, the angle that the tangent to the trajectory makes with the

horizontal. Since v is the velocity of the projectile in the direction of its motion,

tf\ /- a x '

(6) Cos 9--.

(7) Sin 0=?' and if we assume

(8) E = as the ratio between retardation and velocity, we

may write (4) and (5) as follows:

(9) x"=-Ex' (10) y" = E y' g.

In this form the equations are used in the construction of trajec- tories by the method of numerical integration. By reference to (i) we see that,

In this equation, G is a function of the velocity alone, as given in Table I. H is a function of the altitude alone as given by equation (2). C is a function of the weight and form of the projectile as given in equation (3). As in the older ballistic methods, C implicitly includes unknown variations from standard conditions in such quantities as density of the air, moisture in the air, temperature of the air, yaw of the projectile, i.e. angle between the longer axis of the projectile and the tangent to the trajectory. ,