Понятие масштаба. Измерение расстояний на местности и на карте
Самарский областной центр технического творчества учащихся
Самарская городская общественная организация
«Детско-молодежный спортивно-технический клуб Контур»
Абрамов А.В.
Самара, 2000 г.
Спортивная радиопеленгация
1 часть
Пособие для учащихся учреждений дополнительного образования и для занятий спортивной радиопеленгацией в семье
1.4. Понятие масштаба. Измерение расстояний на местности и на карте.
Вспомним материал параграфа 2. Там говорилось о важнейших свойствах карты. Одно из них гласило: все объекты на карте уменьшены по сравнению с соответствующими объектами местности в одинаковое количество раз. А во сколько же раз карта уменьшена по сравнению с местностью? Наверное, разные карты уменьшены по-разному. Величина, характеризующая степень уменьшения карты, называется масштабом.
Масштаб карты — это дробь, в числителе которой стоит единица, а в знаменателе – величина, показывающая, во сколько раз уменьшены объекты карты по сравнению с соответствующими объектами местности.
Масштаб карты указывается в зарамочном оформлении. Знание масштаба позволяет нам измерять расстояния по карте и переводить их в расстояния на местности. В примере, рассмотренном в предыдущем параграфе, мы, двигаясь к лесному озеру, не знали, сколько нам до него идти. Вдруг мы отклонились от азимута и озеро давно уже позади? Такого вопроса не возникло, если бы мы, измерив расстояние от домика лесника до озера по карте, рассчитали это расстояние на местности.
Пусть масштаб карты составляет 1:15000. Это означает, что все расстояния местности уменьшены при нанесении на карту в 15000 раз. Следовательно, расстояния, измеренные по карте, при переносе на местность должны быть увеличены в 15000 раз. Каждый сантиметр карты составляет 15000 сантиметров на местности или 150 метров. Таким образом, для карты масштаба 1:15000, 1 см на карте соответствует 150 метрам на местности, а 1 мм – 15 метрам.
Как перевести расстояние, измеренное по карте, в расстояние на местности? Очень просто. Нужно расстояние в миллиметрах умножить на 15 (вспомните, ведь 1 мм это 15 м). И тогда мы получим расстояние в метрах.
Обратите внимание, что в значении масштаба не указана единица измерения (1:15000). Это не случайно. Дело в том, что нет никакой разницы в каких единицах вести измерения. Хоть в попугаях и слоненках, как это делалось в известном мультфильме. Выражение масштаба показывает, что 1 единица на карте, будь то миллиметр, сантиметр, попугай, соответствует 15000 таких же единиц на местности (миллиметров, сантиметров, попугаев).
Для удобства работы условимся измерять расстояния на карте в миллиметрах, а на местности в метрах. Тогда для перевода единиц карты в единицы местности можно воспользоваться таким соотношением:
Чтобы найти расстояние между двумя объектами местности в метрах, нужно на карте измерить это расстояние в миллиметрах, умножить на знаменатель масштаба и перевести полученный результат в метры, то есть разделить на тысячу.
Запишем соотношение в виде формулы:
где – F(m) – расстояние на местности в метрах,
K(mm) – расстояние по карте в миллиметрах, M – знаменатель масштаба.
Задания для самостоятельной работы.
- Определите расстояния между КП по картам различных масштабов.
- Выберите на карте перегон заданной длины.
- Вдоль тропы установлены КП с номерами. На карточке нарисован отрезок и указан масштаб. Добежать до «своего» КП.
- Добежать до заданного КП. Нарисовать отрезок в разных масштабах.
- Даны направления (азимуты) и расстояния. Найти КП на местности.
- Идти от КП к КП (с точки каждого КП видны другие) и рисовать маршрут в виде ломаной линии при заданном масштабе.
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